×

Non-holonomic Lagrangian and Hamiltonian mechanics: An intrinsic approach. (English) Zbl 1039.37045

Summary: A geometrical approach to Lagrangian and Hamiltonian nonholonomic dynamics is proposed. The construction relies on a revisitation of the Poincaré-Cartan 1-form, leading to the introduction of the concepts of Lagrangian and Hamiltonian pairs and to the implementation of a nonholonomic Legendre map. The relationship with the standard ‘extrinsic’ approach is outlined. A unified ‘canonical framework’, joining both Lagrangian and Hamiltonian aspects, is proposed.

MSC:

37J60 Nonholonomic dynamical systems
70F25 Nonholonomic systems related to the dynamics of a system of particles
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70H03 Lagrange’s equations
70H05 Hamilton’s equations
PDFBibTeX XMLCite
Full Text: DOI