Reduction of constrained systems with symmetries

DOI10.1063/1.532686zbMath0974.37050OpenAlexW2042015302MaRDI QIDQ4701759

Manuel de León, David Martín de Diego, Juan Carlos Marrero, Frans Cantrijn

Publication date: 21 November 1999

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

Full work available at URL: http://hdl.handle.net/10261/21545

zbMATH Keywords

reductionnonholonomic constraintssingular Lagrangian systems

Mathematics Subject Classification ID

Related Items (22)

Geometric Hamilton–Jacobi theory for systems with external forces ⋮ A generalization of Chetaev’s principle for a class of higher order nonholonomic constraints ⋮ Reductions: precontact versus presymplectic ⋮ A historical review on nonholomic mechanics ⋮ Lagrange-d'Alembert-Poincaré equations by several stages ⋮ Unnamed Item ⋮ The geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems: The vakonomic bracket ⋮ Discrete nonholonomic Lagrangian systems on Lie groupoids ⋮ Lagrangian reduction of generalized nonholonomic systems ⋮ Unnamed Item ⋮ Variational development of the semi-symplectic geometry of nonholonomic mechanics ⋮ Symmetry and reduction in implicit generalized Hamiltonian systems ⋮ Singular reduction of implicit Hamiltonian systems ⋮ Birkhoffian formulations of nonholonomic constrained systems ⋮ Reduction of a Hamilton-Jacobi equation for nonholonomic systems ⋮ Symmetries, constants of the motion, and reduction of mechanical systems with external forces ⋮ Reduction of nonholonomic mechanical systems with symmetries ⋮ Adjoint symmetries and the generation of first integrals in non-holonomic mechanics ⋮ Nonholonomic constraints in classical field theories ⋮ Cosymplectic reduction of constrained systems with symmetry ⋮ Hamilton–Jacobi theory for degenerate Lagrangian systems with holonomic and nonholonomic constraints ⋮ Generalized nonholonomic mechanics, servomechanisms and related brackets

Cites Work

• Reduction of some classical non-holonomic systems with symmetry
• Poisson reduction for nonholonomic mechanical systems with symmetry
• Nonholonomic reduction
• Mechanical systems with nonlinear constraints
• Geometry of nonholonomic constraints
• Examples of gauge conservation laws in nonholonomic systems
• The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems
• On the Hamiltonian formulation of nonholonomic mechanical systems
• Reduction of constrained mechanical systems and stability of relative equilibria
• Nonholonomic mechanical systems with symmetry
• Geometric formulation of mechanical systems with one-sided constraints
• A mechanical model with constraints
• Mechanical systems subjected to impulsive constraints
• A differential geometric setting for mixed first- and second-order ordinary differential equations
• A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
• On the geometry of non-holonomic Lagrangian systems

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