Dirac Structures and the Legendre Transformation for Implicit Lagrangian and Hamiltonian Systems

DOI10.1007/978-3-540-73890-9_18zbMath1130.37028OpenAlexW1886873890MaRDI QIDQ5436775

Hiroaki Yoshimura, Jerrold E. Marsden

Publication date: 17 January 2008

Published in: Lagrangian and Hamiltonian Methods for Nonlinear Control 2006 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-73890-9_18

zbMATH Keywords

Hamiltonian formalismnonholonomic systemsconstraintspoint vorticesdegenerate LagrangiansL-C circuitsDirac's theory

Mathematics Subject Classification ID

Hamilton's equations (70H05) Analytic circuit theory (94C05) Constrained dynamics, Dirac's theory of constraints (70H45) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lagrange's equations (70H03)

Related Items

Reduction of Dirac structures and the Hamilton-Pontryagin principle, Dirac structures in nonequilibrium thermodynamics for simple open systems, Variational and geometric structures of discrete Dirac mechanics, Lagrangian and Hamiltonian formulation of transmission line systems with boundary energy flow, Tensor products of Dirac structures and interconnection in Lagrangian mechanics, Hamilton–Jacobi theory for degenerate Lagrangian systems with holonomic and nonholonomic constraints, A generalized nonlinear oscillator from non-standard degenerate Lagrangians and its consequent Hamiltonian formalism

Cites Work

• Dirac structures in Lagrangian mechanics. I: Implicit Lagrangian systems
• Dirac structures in Lagrangian mechanics. II: Variational structures
• Implicit Hamiltonian systems with symmetry
• Singular reduction of implicit Hamiltonian systems
• Generalized Hamiltonian Dynamics
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