Massa, Enrico; Vignolo, Stefano; Bruno, Danilo Non-holonomic Lagrangian and Hamiltonian mechanics: An intrinsic approach. (English) Zbl 1039.37045 J. Phys. A, Math. Gen. 35, No. 31, 6713-6742 (2002). 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. Cited in 12 Documents 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 \textit{E. Massa} et al., J. Phys. A, Math. Gen. 35, No. 31, 6713--6742 (2002; Zbl 1039.37045) Full Text: DOI