converting equation into multiple of two matrix

hi there,

hope you are doing good

guys i want to convert some equations into the multiple of two matrices automatically. for example

it will be appreciated if u will help me.

thanks in advance .

Answer 1

[Torsten]

https://de.mathworks.com/help/symbolic/sym.equationstomatrix.html

[Rahul Jangid]

thanks bro but i need something which can be used with a1 b1 c1 a2 b2 c2 kind of multiplier .

[Torsten]

If you can extract

A = [a1 b1 c1 ; a2 b2 c2]

and

b = [ 0 ; 0]

from your equations

a1*x + b1*y + c1*z = 0
a2*x + b2*y + c2*z = 0

using EquationsToMatrix, isn't that exactly what you want ?

[Rahul Jangid]

thanks bro tomorrow i am trying with

[A,b] = equationsToMatrix(eqns)

and getting error as

Error using mupadengine/feval_internal

Unable to convert to matrix form because the system does not seem to be linear.

Error in sym/equationsToMatrix (line 61)

T = eng.feval_internal('symobj::equationsToMatrix',eqns,vars);

Error in P_rough (line 11)

[A,b] = equationsToMatrix(eqns)

but after using

vars = [x y z]
[A,b] = equationsToMatrix(eqns,vars)

i am getting correct 
thanks for your time

[Torsten]

Of your equations are nonlinear in x,y and z, equationsToMatrix will not work.

Your equations in the graphics you included were linear in x,y and z.

Answer 2

[Rahul Jangid]

HI BRO CAN YOU PLEASE HELP ME WITH THIS IT IS SHOWING SOME ERROR

syms m J x xd TE TEd xb xbd TEb TEbd a b t K1 K2 C1 C2
KE = m*xd^2/2 + J*TEd^2/2;

PE = K1*((x-a*sin(TE))-(xb-a*sin(TEb)))^2/2 + K2*((x+b*sin(TE))-(xb+b*sin(TEb)))^2/2;

R   = C1*((xd-a*cos(TE)*TEd)-(xbd-a*cos(TEb)*TEbd))^2/2 + C2*((xd+b*cos(TE)*TEd)-(xbd+b*cos(TEb)*TEbd))^2/2;

L   = KE-PE;

 %% LagrangeDynamicEqDeriver

q = [x, TE]; Dq = [xd, TEd];       % variables : x and theta


Eq = S_LagrangeDynamicEqDeriver(L, R, q, Dq) == 0

L_q = 

R_Dq = 

L_Dq_dt = 

Eq = 

vars = [xd TEd x TE]

vars = 

[A,b] = equationsToMatrix(Eq,vars)

Error using mupadengine/feval_internal
Unable to convert to matrix form because the system does not seem to be linear.

Error in sym/equationsToMatrix (line 61)
T = eng.feval_internal('symobj::equationsToMatrix',eqns,vars);

Supporting file is

function Eq = S_LagrangeDynamicEqDeriver(L, R, q, Dq)
%%
syms t
N = length(q);
%% Calculation of L_q = r.L/r.q and L_Dq = r.L/r.Dq
L_q = sym(zeros(N,1));
L_Dq = sym(zeros(N,1));
for ii = 1:N
   L_q(ii) = diff(L, q(ii)) ;             % diff. of L                 wrt. q                   one by one
   L_Dq(ii) = diff(L, Dq(ii)) ;           % diff. of gen. coordinate   wrt. q dot               one by one
end

L_q
L_Dq;
%% Calculation of R_q = r.L/r.q and R_Dq = r.L/r.Dq
R_Dq = sym(zeros(N,1));
for ii = 1:N
   R_Dq(ii) = diff(R, Dq(ii));
end
R_Dq
%% Calculation of  L_Dq_dt = qd/dt( r_Dq ) 
L_Dq_dt = sym(zeros(N,1));
for ii = 1:N
    for jj = 1:N
        q_dst = [char(q(jj)), '(t)'];
        Dq_dst = ['diff(', q_dst,',t)'];
        L_Dq(ii)  = subs(L_Dq(ii), {q(jj), Dq(jj)}, {str2sym(q_dst), str2sym(Dq_dst)});
    end
    L_Dq;
    L_Dq_fcn     = symfun(L_Dq(ii), t);
    L_Dq_dt(ii)  = diff(L_Dq_fcn, t);
end
L_Dq_dt

%% Lagrange's equations (Second kind) 
Eq = sym(zeros(N,1));
for ii = 1:N
   Eq(ii) = simplify(L_Dq_dt(ii) + R_Dq(ii) - L_q(ii)) ;
end

end

[Torsten]

Your equations are two second-order differential equations.

EquationsToMatrix can't help to solve it.

Specify 4 boundary conditions and try "dsolve".

If "dsolve" fails (which is probable for such a complicated system), use ode45 or another of the numerical integrators.