# Question:Resolution of differential system with big matrix with trigonometric functions

October 29 2013
Maple

1

Hello,

I look for solving a DAE system i obtain after having determined the equations of a mechanical system with kinematic closed loops.

For that, thanks to the partitioning method, i could transform my DAE in ODE system.

But now, i don't manage to solve my ODE system.

The first issue was the calculation of big matrix with trigonometric functions. With your help in the post "Resolution of a big product of matrix with trigonometric function" (http://www.mapleprimes.com/questions/200012-Rsolution-Of-A-Big-Product-Of-Matrix) , i could calculate the different matrix involved are calculated.

Now, the resolution with my differential system is very long and never finished.

@Carl Love 3670 gives me good advices. He asked me to try to avoid symbolic calculations of the matrix.

Do not use the output option for dsolve.

Then the following procedure evaluates the Matrix AA:

AA:= proc(S,t)
local Cu_inv:= eval(Cu, S(t))^(-1), tCu_inv:= eval(tCu, S(t))^(1);
eval(Avv - Avu.Cu_inv.Cv + tCv.tCu_inv.Auu.Cu_inv.Cv - tCv.tCu_inv.Auv, S(t))
end proc:

To use it, invoke AA(Sol, t) where t is an actual numeric value.

Unfortunately, i don't see how i can use this method for the moment? But, i think that there is a step i don't understand. For me, i have to make the calculation of the big matrix AA and QQ before solving my differentiel system because my differentiel system is composed with AA and QQ.

Here you can find the system i try to solve.

and here you can find the maple file without the steps leading to the setting of the equations

calcul_des_matrices_.mw

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