MSGSS
Polynomial Coefficients of Elimination Results from a system of Classical Mechanics
We study the static solutions of a rotating double pendulum: a double pendulum modeled as constructed from physical pendula, or three-dimensional rigid bodies, and made to rotate uniformly about the vertical axis through the fixed inner pivot. Resultants can be computed to produce bifurcation diagrams: plots of equilibrium positions against a control parameter. Bifurcation can also be described by a system of polynomial equations. The position variables of the pendula can be eliminated from this system to produce a polynomial condition (the resultant) on the parameter space; the model exhibits bifurcation for parameter values which are solutions of this polynomial. This and other related resultants have been computed using DixonEDF, an algorithm which extracts a factorization of the Dixon resultant, and which is implemented in the CAS Fermat. In this presentation, I will also present several observations of novel patterns observed in the coefficient arrays of the large polynomials produced by these computations.