numpy - Differential equations with coupled derivatives in python

Question

I am trying to solve a set of differential equations using sympy and scipy, but cannot figure out how to bring them in the appropriate form. In brief, I have a set of two coupled second order differential equations that I can re-write into a system of four first order differential equations of the form:

dot(x1) = x2

dot(x2) = f(x1, x2, x3, x4, dot(x4))

dot(x3) = x4

dot(x4) = f(x1, x2, x3, x4, dot(x2))

My problem is the coupling of the first derivatives. In Matlab, I can use a time- and state-variable dependent mass matrix to solve this, but in python, I have only seen approaches with a time-invariant mass matrix. Any advice would be much appreciated.

Answer 1

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