Hamel's Equations and Geometric Mechanics of Constrained and Floating Multibody and Space Systems

Abstract

Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's equations, on the other hand, provide a universal approach to non-holonomic mechanics in local coordinates. The link between Hamel's formulation and geometric approaches in local coordinates has not been discussed sufficiently. The reduced Euler-Lagrange equations as well as the curvature of the connection, are derived with Hamel's original formalism. Intrinsic splitting into Euler-Lagrange and Euler-Poincare equations, and inertial decoupling is achieved by means of the locked velocity. Various aspects of this method are discussed.