Anholonomic frames in constrained dynamics

Abstract

We demonstrate the usefulness of anholonomic frames in the contexts of nonholonomic and vakonomic systems. We take a consistently differential-geometric approach. As an application, we investigate the conditions under which the dynamics of the two systems will be consistent. A few illustrative examples confirm the results.

33 pages, to appear in `Dynamical Systems. An international journal.'

References in corpus (6)

• Routh's procedure for non-Abelian symmetry groups
• A Lie algebroid framework for non-holonomic systems
• Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations
• Reduction and reconstruction aspects of second-order dynamical systems with symmetry
• Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations
• Relative equilibria of Lagrangian systems with symmetry

Cited by in corpus (6)

• The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem
• The inverse problem for Lagrangian systems with certain non-conservative forces
• Routh reduction and Cartan mechanics
• Reduction of invariant constrained systems using anholonomic frames
• Implicit Lagrange-Routh Equations and Dirac Reduction
• Geodesic extensions of mechanical systems with nonholonomic constraints