Thread Subject:

Solving a (complicated) equation system

Hello !

I have a quite difficult system of equations to solve. I am desperate to find the solution now to this problem. Here are the equations I have at my disposal :

tan(alphaAR)*(R*cos(beta))==ee
beta==asin((xg-ee)/R)
tan(delta-alphaAV)==((L-ee)/(R*cos(beta)))

I know the values of :

R, xg, alphaAV, L, alphaAR

So basically there are 3 equations with 3 unkown variables.

I want to find the value of beta, ee and delta.

I tried to solve this but without success. Even when I first try to solve the first 3 equations together by doing :

solve(tan(alphaAR)*(Rvirage*cos(beta))==ee,beta==asin((xg-ee)/Rvirage),tan(delta-alphaAV)==((L-ee)/(Rvirage*cos(beta))))

I get an error :

-----------------------------------------------------------
Error using beta (line 21)
Not enough input arguments.

Error in simpletab>finalcheck_Callback (line 2368)
solve(tan(alphaAR)*(Rvirage*cos(beta))==ee,beta==asin((xg-ee)/Rvirage),tan(delta-alphaAV)==((L-ee)/(Rvirage*cos(beta))))

Error in gui_mainfcn (line 96)
        feval(varargin{:});

Error in simpletab (line 22)
    gui_mainfcn(gui_State, varargin{:});

Error in
@(hObject,eventdata)simpletab('finalcheck_Callback',hObject,eventdata,guidata(hObject))

Error while evaluating uicontrol Callback
----------------------------------------------------------------------

Thanks a lot for any help I could get ! :-)

"Matt " <mathieu.horsky@gmail.com> wrote in message
news:jrncrv$cjl$1@newscl01ah.mathworks.com...
> Hello !
>
> I have a quite difficult system of equations to solve. I am desperate to
> find the solution now to this problem. Here are the equations I have at my
> disposal :
>
> tan(alphaAR)*(R*cos(beta))==ee
> beta==asin((xg-ee)/R)
> tan(delta-alphaAV)==((L-ee)/(R*cos(beta)))
>
> I know the values of :
>
> R, xg, alphaAV, L, alphaAR
>
> So basically there are 3 equations with 3 unkown variables.
>
> I want to find the value of beta, ee and delta.
>
> I tried to solve this but without success. Even when I first try to solve
> the first 3 equations together by doing :
>
> solve(tan(alphaAR)*(Rvirage*cos(beta))==ee,beta==asin((xg-ee)/Rvirage),tan(delta-alphaAV)==((L-ee)/(Rvirage*cos(beta))))
>
> I get an error :
>
> -----------------------------------------------------------
> Error using beta (line 21)
> Not enough input arguments.

Define beta to be a symbolic variable. Since you're doing this inside a
function file, I would use SYM instead of SYMS:

beta = sym('beta');
% instead of
syms beta

The latter "poofs" the variable into the workspace at runtime, after MATLAB
has parsed the file. When it parsed the file, MATLAB needed to know to what
the identifier beta referred; since there is a BETA function and nothing
that it could tell indicated that beta should be a variable, it was treated
as a call to the function with 0 inputs. The former makes it clear that beta
is a variable (since it appears on the left side of an equals sign.)

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

Maybe
syms Rvirage, xg, alphaAV, L, alphaAR, beta, ee, delta
solve(tan(alphaAR)*(Rvirage*cos(beta))==ee,beta==asin((xg-ee)/
Rvirage),tan(

Thank you both for the VERY QUICK answers ! I've tried to re-organize a bit the function :

beta = sym('beta');

equ4='tan(alphaAR)==ee/(R*cos(beta))'
equ5='sin(beta)==((xg-ee)/R)'
equ6='tan(delta-alphaAV)==((L-ee)/(R*cos(beta)))'

[beta, delta, ee]=solve(equ4,equ5,equ6,'delta','beta','ee')

Again the following variables are defined previously in the program :

alphaAR, R, xg, alphaAV, L

Now I'm getting the following error, despite the fact that the syntax of that seems allright to me !

-------------------------------------
Error using solve>processString (line 337)
' tan(alphaAR)==ee/(40*cos(beta)) ' is not a valid expression or equation.

Error in solve>getEqns (line 267)
      eqns = processString(eqns, v, vc);

Error in solve (line 150)
[eqns,vars,options] = getEqns(varargin{:});

Error in simpletab>finalcheck_Callback (line 2378)
[beta, delta, ee]=solve(equ4,equ5,equ6,'delta','beta','ee')

Error in gui_mainfcn (line 96)
        feval(varargin{:});

Error in simpletab (line 22)
    gui_mainfcn(gui_State, varargin{:});

Error in
@(hObject,eventdata)simpletab('finalcheck_Callback',hObject,eventdata,guidata(hObject))

Error while evaluating uicontrol Callback
------------------------------------

Thanks a lot again ! :-)

And if I try to add a "d" after all trigonometric functions (since I'm working on degrees), here is what I get (a little bit better) :

Warning: Explicit solution could not be found.
> In solve at 169
  In simpletab>finalcheck_Callback at 2378
  In gui_mainfcn at 96
  In simpletab at 22
  In @(hObject,eventdata)simpletab('finalcheck_Callback',hObject,eventdata,guidata(hObject))
 
beta =
 
[ empty sym ]
 

delta =

     []


ee =

     []

"Matt " <mathieu.horsky@gmail.com> wrote in message
news:jrnf6v$o4p$1@newscl01ah.mathworks.com...
> Thank you both for the VERY QUICK answers ! I've tried to re-organize a
> bit the function :
>
> beta = sym('beta');
>
> equ4='tan(alphaAR)==ee/(R*cos(beta))'

Do not specify your expressions as strings.

Also, this syntax will only work if you're using release R2012a or later, I
believe. For earlier releases, you'd probably want to rearrange this to
read:

equ4 = tan(alphaAR) - ee/(R*cos(beta));

and similarly for the other equations.

> equ5='sin(beta)==((xg-ee)/R)'
> equ6='tan(delta-alphaAV)==((L-ee)/(R*cos(beta)))'
>
> [beta, delta, ee]=solve(equ4,equ5,equ6,'delta','beta','ee')
>
> Again the following variables are defined previously in the program :
>
> alphaAR, R, xg, alphaAV, L

Because you specified your equations as strings, SOLVE cannot "see" those
previously defined values.

*snip*

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

On 18.06.12 16:55, Matt wrote:
> And if I try to add a "d" after all trigonometric functions (since I'm working on degrees), here is what I get (a little bit better) :

sind etc. are currently not supported for symbolic input. I wrote a
little bit about the reasons just recently here; additionally, the error
you received indicates that you tried putting them in a string.


Christopher

Thanks everybody for the help ! I' modified the equation :

beta = sym('beta');
solve(tand(alphaAR)==(xg-R*sind(beta))/(R*cosd(beta)),beta)
assignin('base', 'beta', beta)

If I try to solve it using another math program, I get 2 solutions for this equation, but with Matlab, all I get is :

-----------------------------------------
Undefined function 'sind' for input arguments of type 'sym'.

Error in simpletab>finalcheck_Callback (line 2381)
solve(tand(alphaAR)==(xg-R*sind(betaa))/(R*cosd(betaa)),betaa)

Error in gui_mainfcn (line 96)
        feval(varargin{:});

Error in simpletab (line 22)
    gui_mainfcn(gui_State, varargin{:});

Error in
@(hObject,eventdata)simpletab('finalcheck_Callback',hObject,eventdata,guidata(hObject))

Error while evaluating uicontrol Callback
----------------------------------------

I've read the help section and tried different methods for this, without success !

"Matt " <mathieu.horsky@gmail.com> wrote in message
news:jrrr2l$71n$1@newscl01ah.mathworks.com...
> Thanks everybody for the help ! I' modified the equation :
>
> beta = sym('beta');
> solve(tand(alphaAR)==(xg-R*sind(beta))/(R*cosd(beta)),beta)

Call SOLVE with an output argument.

> assignin('base', 'beta', beta)
>
> If I try to solve it using another math program, I get 2 solutions for
> this equation, but with Matlab, all I get is :
>
> -----------------------------------------
> Undefined function 'sind' for input arguments of type 'sym'.

The degree-based trig functions are not defined for symbolic objects. Solve
using SIN, COS, TAN (which ARE defined for symbolic objects) and then
convert the result from radians to degrees.

*snip*

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

I've converted my equation to radians :

solve(tan(0.02913639281699945036921220856349)==(1-40*sin(beta))/(40*cos(beta)),beta)

But I get the following error :

----------------------------------------------
Error using beta (line 21)
Not enough input arguments.

Error in testequ (line 2)
solve(tan(0.02913639281699945036921220856349)==(1-40*sin(beta))/(40*cos(beta)),beta)
------------------------------------------------

I know the trigonometric equations are kind of annoying to solve since there can be many solutions but there I cannot even get to the point I can calculate this. With Mathematica I can solve but I want to solve this with Matlab.

Thanks a lot for the help ! :)

On 6/28/2012 8:59 AM, Matt wrote:
> I've converted my equation to radians :
>
> solve(tan(0.02913639281699945036921220856349)==(1-40*sin(beta))/(40*cos(beta)),beta)
>
> But I get the following error :
>
> ----------------------------------------------
> Error using beta (line 21)
> Not enough input arguments.
>
> Error in testequ (line 2)
> solve(tan(0.02913639281699945036921220856349)==(1-40*sin(beta))/(40*cos(beta)),beta)
> ------------------------------------------------
>
> I know the trigonometric equations are kind of annoying to solve since there can
> be many solutions but there I cannot even get to the point I can calculate this.
>With Mathematica I can solve but I want to solve this with Matlab.
>
> Thanks a lot for the help ! :)
>

beta is build-in. Use something else.

-------------------
EDU>> syms betaX
EDU>> solve(tan(0.02913639281699945036921220856349)==(1-40*sin(betaX))/(40*cos(betaX)),betaX)
  
ans =
  <snip>
  
EDU>> double ans

ans =

     97 110 115

EDU>>

------------------------


Nasser

Thanks a lot Nasser. But how should I interpret this result (97 110 115) ? What I am looking for is an angle. :-)

On 6/28/2012 2:51 PM, Matt wrote:
> Thanks a lot Nasser. But how should I interpret this result (97 110 115) ? What I am looking for is an angle. :-)
>


try this:

EDU>> solve(tan(0.02913639281699945036921220856349)-(1-40*sin(betaX))/(40*cos(betaX)))
  
ans =
<snip>
  
EDU>> double(ans)

ans =

   -0.0041 + 0.0000i
    3.0875 + 0.0000i

EDU>> real(ans)

ans =

    -0.0041
     3.0875

So that is the solution. in radians. 2 angles.

--Nasser

Thank you, that's the values I was looking for ! :-)

One more question :

How can I automatically take the first value ? In this case the smallest one (-0.0041). I have to make calculations with this value.

Thanks a lot ! :-)

On 7/1/2012 3:01 PM, Matt wrote:
> One more question :
>
> How can I automatically take the first value ? In this case the smallest
>one (-0.0041). I have to make calculations with this value.
>
> Thanks a lot ! :-)
>

use min()?

syms x
EDU>> sol=solve(tan(0.02913639281699945036921220856349)-(1-40*sin(x))/(40*cos(x)));
EDU>> sol=double(sol);
EDU>> sol=real(sol);
EDU>> sol_small=min(sol)

sol_small =

    -0.0041

EDU>> sol_large=max(sol)

sol_large =

     3.0875

Yes it is just what I figured out few minutes ago ! But you have been of a very good help Nasser ! Thanks a lot ! :-)

"Matt" wrote in message <jshnvc$6mf$1@newscl01ah.mathworks.com>...
> I've converted my equation to radians :
>
> solve(tan(0.02913639281699945036921220856349)==(1-40*sin(beta))/(40*cos(beta)),beta)

Although the equations

tan(A)*R*cos(x) = E
R*sin(x) = G-E

Can be reduced to

tan(A) = (G-R*sin(x)/(R*cos(x)

They can also be reduced to

sin(x+A) = G*cos(A)/R

which leads to the simple solution

x = - A + asin( G * cos( A ) / R )

Hope this helps.

Greg

Greg