# High-dimensional second-order differential matrix equations

I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known:

$$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$$

where $$q=[\dot{\omicron}_{3\times1},\dot{\omega}_{3\times1},\dot{\Omega}_{3\times1},\omicron_{3\times1},\omega_{3\times1},\Omega_{3\times1}]$$

In here, the matrices $$M(q)$$, $$C(q,\dot{q})$$ are $$18 \times 18$$ matrices, and $$G(q)$$ are $$18 \times 1$$ vector)

I still cannot describe the matrices explicitly, because I have not completed work in this direction, but I see in advance that a system of equations of such a large dimension can cause computational problems.

Especially difficulties can be added by the fact that the matrices $$M(q)$$, $$C(q,\dot{q})$$ and the vector $$G(q)$$ are nonstationary, which will complicate the already complex equations of motion.

Which $$numerical$$ methods do you suggest to solve the following matrix diff. equation? And why?

I will start working for now and will supplement the question as it develops.

Remark: I have a Ryzen 7 2700 Pro based PC with 8 cores and 16 threads + 16 GB of RAM.

• See for instance mathematica.stackexchange.com/questions/208590/… Jul 17 '21 at 13:43
• @AlexTrounev Thanks for the tip, I'll try to come up with a suitable computational procedure.
– dtn
Jul 17 '21 at 17:43