Nonholonomic constraints in time-dependent mechanics

DOI10.1063/1.532808zbMath0976.70010arXivmath-ph/9807014OpenAlexW3104949547MaRDI QIDQ4701794

Luigi Mangiarotti, Gennadi A. Sardanashvily, Giovanni Giachetta

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/9807014

zbMATH Keywords

Hamiltonian formalismconfiguration bundleconstraint reaction forcevertical tangent bundleideal nonholonomic constraintstime-dependent nonholonomic mechanics

Mathematics Subject Classification ID

Hamilton's equations (70H05) Constrained dynamics, Dirac's theory of constraints (70H45) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Nonholonomic systems related to the dynamics of a system of particles (70F25)

Related Items (11)

On the Lagrangian form of the variational equations of Lagrangian dynamical systems ⋮ Iper-ideal kinetic constraints in continuum mechanics ⋮ Theoretical analysis for a class of rheonomous affine constraints on configuration manifolds. II: Foliation structures and integrating algorithms ⋮ Theoretical analysis for a class of rheonomous affine constraints on configuration manifolds. I: Fundamental properties and integrability/nonintegrability conditions ⋮ Lagrangian description of the variational equations ⋮ On the geodesic form of second-order dynamic equations ⋮ Constraints in Hamiltonian time-dependent mechanics ⋮ Classical and quantum mechanics with time-dependent parameters ⋮ Jacobi equations using a variational principle ⋮ Symmetry and conservation laws in non-holonomic mechanics ⋮ Jacobi fields of completely integrable Hamiltonian systems

Cites Work

• Mechanical systems with nonlinear constraints
• Reduction of constrained mechanical systems and stability of relative equilibria
• On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints
• Non-standard connections in classical mechanics
• Jet methods in nonholonomic mechanics
• Geometric formulation of mechanical systems subjected to time-dependent one-sided constraints
• Hamiltonian time-dependent mechanics
• Mechanical systems with nonholonomic constraints
• A geometrical framework for the study of non-holonomic Lagrangian systems: II
• Lagrangian systems with constraints: a geometric approach to the method of Lagrange multipliers
• Non-holonomic Lagrangian systems in jet manifolds
• A geometrical framework for the study of non-holonomic Lagrangian systems
• On the geometry of non-holonomic Lagrangian systems

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