Riemannian cubic polynomials

Abstract

This paper gives an analysis of the Riemannian cubic polynomials, with special interest in the Lie group SO(3), based on the study of a second order variational problem. The corresponding Euler-Lagrange equation gives rise to an interesting system of nonlinear di erential equations. Motivated by the problem of the motion of a rigid body, the reduction of the essential size and the separation of the variables of the system are obtained by means of invariants along the cubic polynomials.