How to solve this simple system of 2 equation in MATLAB

Question

Abdulaziz Abutunis 2018-5-4

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评论： John BG 2018-5-10

Hi All;

I wonder if Matlab can solve this two equations to find the Fx and Fy as a function in the other constants. I know I can do it by hand just want to validate. Please see the initial code below

syms D L COST SINT Fx Fy
Fx * COST + Fy *SINT - D =0; 
Fx * SINT + Fy * COST -L =0;
solve ( text: the two equations for Fx and Fy)

Thank you for your valuable suggestion

Aziz

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Answer 1

John BG 2018-5-6

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编辑：John BG 2018-5-6

在 MATLAB Online 中打开

Hi Abdulaziz

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

syms v Fx Fy D L
  b=[D ;L]
  b =
   D
   L
  A=[(1-v^2)^.5 v;v (1-v^2)^.5]
  A =
  [ (1 - v^2)^(1/2),               v]
  [               v, (1 - v^2)^(1/2)]
  F=A\b
   =
   (D*v^2 - D + L*v*(1 - v^2)^(1/2))/((1 - v^2)^(1/2)*(2*v^2 - 1))
                             (D*v - L*(1 - v^2)^(1/2))/(2*v^2 - 1)

.

these are the expressions

.

    Fx=F(1)
     =
    (D*v^2 - D + L*v*(1 - v^2)^(1/2))/((1 - v^2)^(1/2)*(2*v^2 - 1))
     Fy=F(2)
    Fy =
    (D*v - L*(1 - v^2)^(1/2))/(2*v^2 - 1)

.

with

v=sin(t)

.

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

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Answer 2

Stephan 2018-5-4

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编辑：Stephan 2018-5-4

在 MATLAB Online 中打开

Hi,

you could do so:

% declare syms
syms D L t;
% Coefficient Matrix
A = [cos(t) sin(t); sin(t) cos(t)];
% RHS
b = [D ; L];
% Unknown: Fx, Fy
F = A\b;
% create Matlab function
fun = matlabFunction(F);
% Test for D = 0, L = -1 and t = pi()
D = 0;
L = -1;
t = pi();
[F] = fun(D, L, t)