Numerical work with sagemath 11: Tetrahedron Dynamics

This week I’ve been following up some of the mathematical physics seen in the paper Background independence in a nutshell: the dynamics of a tetrahedron. I have have been looking at how sagemath and python handle polyhedra.

So I’ve written a sagemath program to simulate the dynamics of the classical tetrahedon:

Background independence fig1 which governed by the equations:

Background independence equ2

As a sagemath program this gives:

sagemath11fig1

Typical results are tabulated below showing the behaviour long times T, as theta C tends to 90 degrees.

sagemath11fig2

As part of this work of been developing some python functions in particular a function which will produce the equation of a plane through three points . This is especially useful  for finding the dihedral angle in polyhedra.

sagemath11fig3

sagemath11fig5

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