How do you solve a system of 16 nonlinear equations with 16 unknowns ?

5 views (last 30 days)
taha
taha on 28 Jan 2024
Commented: Walter Roberson on 28 Jan 2024
Ran in:
I am dealing with a system of 16 equations (CL) with 16 variables (A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 F1 E2 F2) and aim to solve it for plotting de w1 w2 w3 w4 w5. However, the solutions I'm finding are not converging, hindering the graph plotting.
I have even tried converting the system into a matrix [A]*[B]=0.
Do you have any ideas about other methods ?
kk=0.1366;
syms A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 E1 E2 F1 F2
CL1 = F1 - (7558294066935945*F1*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E1*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0;
CL2 = F2 - (7558294066935945*F2*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E2*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0;
CL3 = F1*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E1*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0;
CL4 = F2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E2*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0;
CL5 = A1 + C1 == 0;
CL6 = A3*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + C3*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + B3*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + D3*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) == 0;
CL7 = (1142341796335433*pi*A1*kk)/17592186044416 - (1142341796335433*pi*C1*kk)/17592186044416 == 0;
CL8 = (1142341796335433*A3*kk*pi*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*C3*kk*pi*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 + (1142341796335433*B3*kk*pi*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*D3*kk*pi*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 == 0;
CL9 = A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A2*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C2*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B2*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D2*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0;
CL10 = B1*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B2*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D1*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D2*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A1*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A2*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C1*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C2*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0;
CL11 = (1142341796335433*A1*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A2*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C1*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C2*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B1*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B2*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D1*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D2*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0;
CL12 = A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A3*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C3*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B3*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D3*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0;
CL13 = B2*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B3*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D2*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D3*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A2*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A3*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C2*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C3*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0;
CL14 = (1142341796335433*A2*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A3*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C2*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C3*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B2*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B3*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D2*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D3*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0;
CL15 = ((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B1*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B2*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D1*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D2*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A1*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A2*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C1*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C2*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E1*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F1*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0;
CL16 = ((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B2*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B3*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D2*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D3*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A2*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A3*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C2*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C3*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E2*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F2*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0;
solutions = solve([CL1, CL2, CL3, CL4, CL5, CL6, CL7, CL8, CL9, CL10, CL11, CL12, CL13, CL14, CL15, CL16, ], [A1, B1, C1, D1, A2, B2, C2, D2, A3, B3, C3, D3, E1, E2, F1, F2]);
A1_sol = solutions.A1
A1_sol = 
0
B1_sol = solutions.B1
B1_sol = 
0
C1_sol = solutions.C1
C1_sol = 
0
D1_sol = solutions.D1
D1_sol = 
0
A2_sol = solutions.A2
A2_sol = 
0
B2_sol = solutions.B2
B2_sol = 
0
C2_sol = solutions.C2
C2_sol = 
0
D2_sol = solutions.D2
D2_sol = 
0
A3_sol = solutions.A3
A3_sol = 
0
B3_sol = solutions.B3
B3_sol = 
0
C3_sol = solutions.C3
C3_sol = 
0
D3_sol = solutions.D3
D3_sol = 
0
E1_sol = solutions.E1
E1_sol = 
0
F1_sol = solutions.F1
F1_sol = 
0
E2_sol = solutions.E2
E2_sol = 
0
F2_sol = solutions.F2
F2_sol = 
0
xa = (0):0.01:(1/3);
xb = (1/3):0.01:(2/3);
xc = (2/3):0.01:(1);
xd = (0):0.01:(1/3);
xe = (2/3):0.01:(1);
bab=pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2);
cac=(4*pi*13^(1/2)*15^(1/2)*kk)/75;
N1 = -(7558294066935945*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312));
N2 = -(7558294066935945*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312));
w1 = A1_sol * cosh(bab*xa) + B1_sol * sinh(bab*xa) + C1_sol * cos(bab*xa) + D1_sol * sin(bab*xa);
w2 = A2_sol * cosh(bab*xb) + B2_sol * sinh(bab*xb) + C2_sol * cos(bab*xb) + D2_sol * sin(bab*xb);
w3 = A3_sol * cosh(bab*xc) + B3_sol * sinh(bab*xc) + C3_sol * cos(bab*xc) + D3_sol * sin(bab*xc);
w4 = E1_sol *sin(cac*xd) + F1_sol *cos(cac*xd) + E1_sol *N1 + F1_sol *N2 ;
w5 = E2_sol *sin(cac*xe) + F2_sol *cos(cac*xe) + E2_sol *N1 + F2_sol *N2 ;
figure
plot(xa, w1, xb, w2, xc, w3, xd, w4, xe, w5)
  4 Comments
Show 2 older comments
Walter Roberson
Walter Roberson on 28 Jan 2024
You need to take precautions to get the equations entered properly.
kk = sym(1366)/sym(10000);
syms A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 E1 E2 F1 F2
CL1 = str2sym('F1 - (7558294066935945*F1*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E1*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0');
CL2 = str2sym('F2 - (7558294066935945*F2*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E2*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0');
CL3 = str2sym('F1*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E1*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0');
CL4 = str2sym('F2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E2*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0');
CL5 = str2sym('A1 + C1 == 0');
CL6 = str2sym('A3*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + C3*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + B3*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + D3*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) == 0');
CL7 = str2sym('(1142341796335433*pi*A1*kk)/17592186044416 - (1142341796335433*pi*C1*kk)/17592186044416 == 0');
CL8 = str2sym('(1142341796335433*A3*kk*pi*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*C3*kk*pi*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 + (1142341796335433*B3*kk*pi*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*D3*kk*pi*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 == 0');
CL9 = str2sym('A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A2*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C2*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B2*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D2*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0')
CL10 = str2sym('B1*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B2*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D1*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D2*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A1*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A2*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C1*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C2*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0');
CL11 = str2sym('(1142341796335433*A1*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A2*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C1*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C2*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B1*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B2*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D1*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D2*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0');
CL12 = str2sym('A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A3*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C3*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B3*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D3*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0');
CL13 = str2sym('B2*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B3*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D2*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D3*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A2*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A3*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C2*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C3*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0');
CL14 = str2sym('(1142341796335433*A2*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A3*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C2*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C3*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B2*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B3*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D2*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D3*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0');
CL15 = str2sym('((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B1*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B2*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D1*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D2*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A1*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A2*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C1*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C2*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E1*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F1*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0');
CL16 = str2sym('((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B2*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B3*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D2*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D3*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A2*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A3*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C2*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C3*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E2*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F2*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0');
eqns = subs([CL1, CL2, CL3, CL4, CL5, CL6, CL7, CL8, CL9, CL10, CL11, CL12, CL13, CL14, CL15, CL16 ]).'
solutions = solve(eqns, [A1, B1, C1, D1, A2, B2, C2, D2, A3, B3, C3, D3, E1, E2, F1, F2]);
A1_sol = solutions.A1
B1_sol = solutions.B1
C1_sol = solutions.C1
D1_sol = solutions.D1
A2_sol = solutions.A2
B2_sol = solutions.B2
C2_sol = solutions.C2
D2_sol = solutions.D2
A3_sol = solutions.A3
B3_sol = solutions.B3
C3_sol = solutions.C3
D3_sol = solutions.D3
E1_sol = solutions.E1
F1_sol = solutions.F1
E2_sol = solutions.E2
F2_sol = solutions.F2
xa = (0):0.01:(1/3);
xb = (1/3):0.01:(2/3);
xc = (2/3):0.01:(1);
xd = (0):0.01:(1/3);
xe = (2/3):0.01:(1);
bab=pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2);
cac=(4*pi*13^(1/2)*15^(1/2)*kk)/75;
N1 = -(7558294066935945*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312));
N2 = -(7558294066935945*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312));
w1 = A1_sol * cosh(bab*xa) + B1_sol * sinh(bab*xa) + C1_sol * cos(bab*xa) + D1_sol * sin(bab*xa);
w2 = A2_sol * cosh(bab*xb) + B2_sol * sinh(bab*xb) + C2_sol * cos(bab*xb) + D2_sol * sin(bab*xb);
w3 = A3_sol * cosh(bab*xc) + B3_sol * sinh(bab*xc) + C3_sol * cos(bab*xc) + D3_sol * sin(bab*xc);
w4 = E1_sol *sin(cac*xd) + F1_sol *cos(cac*xd) + E1_sol *N1 + F1_sol *N2 ;
w5 = E2_sol *sin(cac*xe) + F2_sol *cos(cac*xe) + E2_sol *N1 + F2_sol *N2 ;
figure
plot(xa, w1, xb, w2, xc, w3, xd, w4, xe, w5)

Sign in to comment.

Sign in to answer this question.

Answers (1)

John D'Errico
John D'Errico on 28 Jan 2024
Edited: John D'Errico on 28 Jan 2024
Ran in:
Whenever we see a number supplied to FOUR significant digits, we should expect that is not the true value, but only an approximation, rounded to that value. And that is a bad thing. Is kk known to be EXACTLY that number? We should really think of kk as some (ANY!) number in the interval (0.13655,0.13665). Oh well. See where we get with kk at the given value, then we can worry about if kk is really known to be what you think it is.
Anyway, you have a linear system, once kk is defined. It is not nonlinear.
kk=0.1366;
syms A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 E1 E2 F1 F2
CL(1) = F1 - (7558294066935945*F1*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E1*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0;
CL(2) = F2 - (7558294066935945*F2*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E2*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0;
CL(3) = F1*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E1*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0;
CL(4) = F2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E2*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0;
CL(5) = A1 + C1 == 0;
CL(6) = A3*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + C3*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + B3*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + D3*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) == 0;
CL(7) = (1142341796335433*pi*A1*kk)/17592186044416 - (1142341796335433*pi*C1*kk)/17592186044416 == 0;
CL(8) = (1142341796335433*A3*kk*pi*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*C3*kk*pi*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 + (1142341796335433*B3*kk*pi*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*D3*kk*pi*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 == 0;
CL(9) = A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A2*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C2*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B2*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D2*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0;
CL(10) = B1*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B2*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D1*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D2*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A1*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A2*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C1*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C2*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0;
CL(11) = (1142341796335433*A1*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A2*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C1*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C2*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B1*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B2*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D1*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D2*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0;
CL(12) = A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A3*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C3*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B3*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D3*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0;
CL(13) = B2*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B3*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D2*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D3*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A2*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A3*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C2*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C3*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0;
CL(14) = (1142341796335433*A2*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A3*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C2*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C3*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B2*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B3*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D2*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D3*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0;
CL(15) = ((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B1*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B2*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D1*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D2*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A1*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A2*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C1*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C2*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E1*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F1*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0;
CL(16) = ((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B2*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B3*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D2*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D3*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A2*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A3*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C2*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C3*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E2*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F2*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0;
[M,rhs] = equationsToMatrix(CL,[A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 E1 E2 F1 F2]);
rhs
rhs = 
We see it is a homogeneous system. So the right hand side is all zeros. If M is singular, then a non-trivial solution exists, and ONLY exists if M is singular. This is a basic characeristic of a homogeneous system of linear equations. M is 16x16.
size(M)
ans = 1×2
16 16
If the rank of M is 16, then you are in trouble.
rank(M)
ans = 16
M has full rank. This means the ONLY solution is all zeros. Just basic linear algebra 101 here I'm afraid. There are no other solutions to the posed system. EVER.
Ok, we said before that kk is given to only 4 significant digits. How close to singular is M? Suppose kk was really some other number in that interval? Might that have changed things?
s = svd(double(M));
format long g
s([1,end-1,end])
ans = 3×1
1.0e+00 * 3928.12115846104 0.00612395922093247 3.23098789983914e-05
We see here the smallest singluar value is close to zero, but not too close. What matters is the ratio of the largest and the smallest singular values. In double precision, that needs to be near 1/eps if the matrix is considered numerically singular. Here the ratio is roughly 1e8. So not even remotely close to singularity.
BUT............
I see things like this:
cos((1234829426200219*kk)/527765581332480))
And while that is only a fragment, if there were some value of kk that is close to kk, where the argument to a cosine is near zero, then we have a second order thing going on. So, is there some value of kk in the interval (0.13655,0.13665), that makes this matrix singular? Best would be to apply fminbnd to the problem. I'll redo the above, but with kk as an unknown variable.
kkint= [0.13655,0.13665];
syms kk
syms A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 E1 E2 F1 F2
CL(1) = F1 - (7558294066935945*F1*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E1*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0;
CL(2) = F2 - (7558294066935945*F2*((5875287987476493*cos((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*cos((1234829426200219*kk)/527765581332480))/3 - (3204841085288823*sin((1234829426200219*kk)/527765581332480))/(234187180623265792*kk*pi) + 5875287987476493/1152921504606846976))/((231133482855809248*kk^2)/75 - 4363783114159819) - (7558294066935945*E2*((5875287987476493*sin((1234829426200219*kk)/527765581332480))/1152921504606846976 - (3^(1/2)*sin((1234829426200219*kk)/527765581332480))/3 + (820439317833938688*cos((1234829426200219*kk)/527765581332480) - 820439317833938688)/(59951918239556042752*kk*pi)))/((231133482855809248*kk^2)/75 - 4363783114159819) == 0;
CL(3) = F1*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E1*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0;
CL(4) = F2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (9*C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 - (9*A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/4 + E2*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75) - (7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) - (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) == 0;
CL(5) = A1 + C1 == 0;
CL(6) = A3*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + C3*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + B3*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) + D3*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)) == 0;
CL(7) = (1142341796335433*pi*A1*kk)/17592186044416 - (1142341796335433*pi*C1*kk)/17592186044416 == 0;
CL(8) = (1142341796335433*A3*kk*pi*cosh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*C3*kk*pi*cos(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 + (1142341796335433*B3*kk*pi*sinh(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 - (1142341796335433*D3*kk*pi*sin(pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2)))/17592186044416 == 0;
CL(9) = A1*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A2*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C1*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C2*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B1*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B2*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D1*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D2*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0;
CL(10) = B1*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B2*pi^(1/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D1*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D2*pi^(1/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A1*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A2*pi^(1/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C1*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C2*pi^(1/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0;
CL(11) = (1142341796335433*A1*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A2*kk*pi*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C1*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C2*kk*pi*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B1*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B2*kk*pi*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D1*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D2*kk*pi*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0;
CL(12) = A2*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - A3*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + C2*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - C3*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + B2*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - B3*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) + D2*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) - D3*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3) == 0;
CL(13) = B2*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - B3*pi^(1/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + D2*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - D3*pi^(1/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + A2*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - A3*pi^(1/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) - C2*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) + C3*pi^(1/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(1/2) == 0;
CL(14) = (1142341796335433*A2*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*A3*kk*pi*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*C2*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*C3*kk*pi*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*B2*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*B3*kk*pi*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 - (1142341796335433*D2*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 + (1142341796335433*D3*kk*pi*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3))/17592186044416 == 0;
CL(15) = ((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F1*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E1*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B1*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B2*pi^(3/2)*cosh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D1*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D2*pi^(3/2)*cos((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A1*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A2*pi^(3/2)*sinh((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C1*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C2*pi^(3/2)*sin((pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E1*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F1*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0;
CL(16) = ((39751161341439*3^(1/2))/1801439850948198400 + 90071873293925895683/180143985094819840000)*((3^(1/2)*((7558294066935945*F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312)) + (7558294066935945*E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi)))/(562949953421312*((208*kk^2*pi^2)/375 - 4363783114159819/562949953421312))))/3 + F2*((5875287987476493*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 - (29376439937382465*13^(1/2)*15^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/(29975959119778021376*kk*pi) + 5875287987476493/1152921504606846976) + E2*((5875287987476493*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/1152921504606846976 - (3^(1/2)*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/3 + (29376439937382465*13^(1/2)*15^(1/2)*(2*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75) - 2))/(59951918239556042752*kk*pi))) + (161*B2*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*B3*pi^(3/2)*cosh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*D2*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*D3*pi^(3/2)*cos((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*A2*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*A3*pi^(3/2)*sinh((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 + (161*C2*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (161*C3*pi^(3/2)*sin((2*pi^(1/2)*((1142341796335433*kk)/17592186044416)^(1/2))/3)*((1142341796335433*kk)/17592186044416)^(3/2))/56457 - (3031766714669543*13^(1/2)*15^(1/2)*E2*kk*pi*cos((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 + (3031766714669543*13^(1/2)*15^(1/2)*F2*kk*pi*sin((4*pi*13^(1/2)*15^(1/2)*kk)/75))/86469112845513523200 == 0;
[M,rhs] = equationsToMatrix(CL,[A1 B1 C1 D1 A2 B2 C2 D2 A3 B3 C3 D3 E1 E2 F1 F2]);
Assuming the maximum singlar value of M will not change by much, lets just see if we can make the smallest singular value close to zero. I could also try to maximize the condition number of M, as a function of kk.
Mfun = matlabFunction(M);
fun = @(KK) min(svd(Mfun(KK)));
fplot(fun,[0.136,0.137])
Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.
And indeed, it does seem as if there is a value of kk that makes the matrix singular. BUT, it is not in the interval we would have expected merely by rounding. We can use a solver to find the value necessary for success. kk needs to be
opts = optimset('fminbnd');
opts.TolX = 1e-13;
[kkval,fval] = fminbnd(fun,0.136,0.137,opts)
kkval =
0.136050001460989
fval =
2.01510175497338e-11
So if kk is instead approximately 0.136050001461293..., then the matrix will be singular. In that case, we would have a valid, non-trivial solution. But you need to recognize that this is very much outside of the interval we expect. Well, at least 10 times farther out than we expect due to a simple rounding operation. In this context, it is far. So, when kk takes on that value, what do we get? Normally, you could just do this:
null(Mfun(kkval))
ans = 16×0 empty double matrix
But even kkval was still not close enough. Instead, since the matrix is now so close to singular, we can take the singular vector corresponding to the smallest singular value.
[U,S,V] = svd(Mfun(kkval));
sol = V(:,end)
sol = 16×1
-1.10319035457962e-12 -0.00064489889211329 -1.10826831611686e-12 -0.00233860846357236 -0.00898763065235101 0.00889548126594225 0.0031454436920399 -0.00174908932897355 -0.0625749846199522 0.0625783077013893
And that is the set of parameters for your unknowns, that WOULD solve the homogeneous problem in a non-trivial way, if kk actually had the value we chose at the end. So if we can modify your equations in a subtle way, by changing the value of kk, to the only value where a non-trivial solution does exist. Possibly the error in your value of kk was a transcription error. I say that since the real value should be more like 0.1360, not 0.1366. Even then, you need the actual value of kk, if you wanted to use null.

Categories

Find more on Quaternion Math in Help Center and File Exchange

Tags

Products


Release

R2023b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!