The geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems: The vakonomic bracket
From MaRDI portal
Publication:2737921
DOI10.1063/1.533229zbMath0995.37048OpenAlexW1971733931MaRDI QIDQ2737921
Manuel de León, Sonia Martínez, Jorge Cortés
Publication date: 30 August 2001
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/10261/21695
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 dynamical systems (37J60)
Related Items (11)
Continuous and discrete approaches to vakonomic mechanics ⋮ A historical review on nonholomic mechanics ⋮ General symmetries in optimal control ⋮ Generalized variational calculus for continuous and discrete mechanical systems ⋮ Symmetries in vakonomic dynamics: Applications to optimal control ⋮ ON THE LAGRANGIAN AND HAMILTONIAN FORMULATION OF A SCALAR FREE FIELD THEORY AT NULL INFINITY ⋮ Discrete vakonomic mechanics ⋮ Optimal control, contact dynamics and Herglotz variational problem ⋮ Constrained Lagrangian dissipative contact dynamics ⋮ Dirac structures in vakonomic mechanics ⋮ Complete inequivalence of nonholonomic and vakonomic mechanics
Cites Work
- Reduction of degenerate Lagrangian systems
- Reduction of some classical non-holonomic systems with symmetry
- Nonholonomic reduction
- Mechanical systems with nonlinear constraints
- Geometry of nonholonomic constraints
- 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
- On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints
- Nonholonomic mechanical systems with symmetry
- Variational principles for constrained systems: Theory and experiment
- Geometric theory of the equivalence of Lagrangians for constrained systems
- On almost-Poisson structures in nonholonomic mechanics
- Dirac Brackets in Constrained Dynamics
- Reduction of constrained systems with symmetries
- Comments on the presymplectic formalism and the theory of regular Lagrangians with constraints
- On the geometry of non-holonomic Lagrangian systems
This page was built for publication: The geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems: The vakonomic bracket
