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–Poincaré equations and inertial decoupling is achieved by means of the locked velocity. Various aspects of this method are discussed.