Solve the chain rule in lagrange equation
3 views (last 30 days)
Show older comments
siti khadijah
on 14 Apr 2016
Commented: siti khadijah
on 6 May 2016
Hai guys,
I would like to ask your opinion about this matter. I have a code as shown below which basically, is the Lagrange equation. I have reached to the Lagrange equation and next, I would like to differentiate the Lagrange equation.
Basically, the Lagrange eqaution is as :
L = KE - PE
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/161221/image.gif)
As shown in the pic, now, I would like to differentiate the L to the r_dot. Could anyone advice me? I have try several ways, but it does not give me the correct answer. Thanks in advance
Regards,
Siti
syms x1(t) x2(t) x3(t) x4(t)
syms a la
syms m1 m2 m3 m4 I1 I2 I3 I4
syms g h1 h2 h3 h4
T0_1=[cos(x1(t)) 0 sin(x1(t)) 0 ;
sin(x1(t)) 0 -cos(x1(t)) 0;
0 1 0 0;
0 0 0 1;];
T1_2=[cos(x2(t)) 0 sin(x2(t)) 0;
sin(x2(t)) 0 -cos(x2(t)) 0;
0 1 0 0;
0 0 0 1;];
T2_3=[cos(x3(t)) 0 sin(x3(t)) 0;
sin(x3(t)) 0 -cos(x3(t)) 0;
0 1 0 -a;
0 0 0 1;];
T3_4=[cos(x4(t)) 0 -sin(x4(t)) -la*cos(x4(t));
sin(x4(t)) 0 cos(x4(t)) -la*sin(x4(t));
0 -1 0 0;
0 0 0 1;];
T1 = T0_1;
T2 = T1*T1_2;
T3 = T2*T2_3;
T4 = T3*T3_4;
xT1 = T1(1,4);
xT1_dot(t) = diff(xT1);
yT1 = T1(2,4);
yT1_dot(t) = diff(yT1);
xT2 = T2(1,4);
xT2_dot(t) = diff(xT2);
yT2 = T2(2,4);
yT2_dot(t) = diff(yT2);
xT3 = T3(1,4)
xT3_dot(t) = diff(xT3);
yT3 = T3(2,4);
yT3_dot(t) = diff(yT3);
xT4 = T4(1,4);
xT4_dot(t) = diff(xT4);
yT4 = T4(2,4);
yT4_dot(t) = diff(yT4);
% v1 = simplify((xT1_dot(t) + yT1_dot(t))^2);
% v2 = simplify((xT2_dot(t) + yT2_dot(t))^2);
% v3 = simplify((xT3_dot(t) + yT3_dot(t))^2);
% v4 = simplify((xT4_dot(t) + yT4_dot(t))^2);
v1 = ((xT1_dot(t) + yT1_dot(t))^2);
v2 = ((xT2_dot(t) + yT2_dot(t))^2);
v3 = ((xT3_dot(t) + yT3_dot(t))^2);
v4 = ((xT4_dot(t) + yT4_dot(t))^2);
KE = (1/2)*m1*v1 + (1/2)*m2*v2 + (1/2)*m3*v3 + (1/2)*m4*v4 + ...
(1/2)*I1*diff(x1(t), t) + (1/2)*I2*diff(x2(t), t) + (1/2)*I3*diff(x3(t), t) + (1/2)*I4*diff(x4(t), t) ;
PE = m1*g*h1 + m2*g*h2 + m3*g*h3 + m4*g*h4 ;
Lag = KE - PE;
0 Comments
Accepted Answer
More Answers (0)
See Also
Categories
Find more on Symbolic Math Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!