Kenneth R. Ball, North Carolina State University


The Hamilton-Pontryagin Principle and the Hamel Equations

Abstract: The Hamilton-Pontryagin principle originated in a recent work of Yoshimura and Marsden. The key idea is that the Euler-Lagrange equations can be derived by extremizing the action of a mechanical system while taking variations of coordinates, velocities, and momenta independently. In this poster we describe the derivation of Hamel equations, that is, the equations of motion projected onto a frame of non-commuting vector fields, and the Hamel coefficients that appear in these equations using the Hamilton-Pontryagin formalism. We then show how our derivation reduces to the Euler-Poincare case when the configuration space is a Lie group and Lagrangian is invariant; and how this formalism is used in dynamics of systems with velocity constraints. We provide simple, illustrative examples such as rotating and sliding rigid bodies.

Advisor: Dmitry Zenkov (North Carolina State University)