Asymptotics of Null Lie Quadratics in $E^3$

Abstract

Lie quadratics are curves in Lie algebras, arising from studies in the mid-1980s of motion planning for rigid bodies. Attention has focused on Lie quadratics in Euclidean 3-space $E^3$ (with cross-product as Lie bracket), especially the codimension-3 subclass of null Lie quadratics in $E^3$. The present paper substantially improves known asymptotic results for this subclass, to an extent that the new results apply to asymptotic dynamics of spherically symmetric rigid balls in classical mechanics.