converting equation into multiple of two matrix

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Rahul Jangid
Rahul Jangid 2023-1-5
评论： Torsten 2023-1-6
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 .

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Torsten
Torsten 2023-1-5
  4 个评论
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Rahul Jangid
Rahul Jangid 2023-1-6
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
Torsten 2023-1-6
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.

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更多回答（1 个）

Rahul Jangid
Rahul Jangid 2023-1-6
编辑：Torsten 2023-1-6
Ran in:
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
  1 个评论
Torsten
Torsten 2023-1-6
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.

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