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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.

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