Symmetries in vakonomic dynamics: Applications to optimal control

DOI10.1016/S0393-0440(00)00069-3zbMath1022.70014OpenAlexW2093019195MaRDI QIDQ5943190

Jorge Cortés, Manuel de León, Sonia Martínez

Publication date: 9 June 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0393-0440(00)00069-3

zbMATH Keywords

symmetryoptimal controlconstrained variational problemkinematic locomotion systemsNoether-type theoremssingular Lagrangian systemsvakonomic dynamics

Mathematics Subject Classification ID

Control of mechanical systems (70Q05) Existence theories for optimal control problems involving ordinary differential equations (49J15) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items

Remarks on multisymplectic reduction ⋮ Variational integrators in discrete vakonomic mechanics ⋮ A historical review on nonholomic mechanics ⋮ Motion measurement of a two-wheeled skateboard and its dynamical simulation ⋮ Geometric reduction in optimal control theory with symmetries ⋮ General symmetries in optimal control ⋮ The Boltzmann-Hamel equations for the optimal control of mechanical systems with nonholonomic constraints ⋮ Discrete vakonomic mechanics ⋮ Optimal control, contact dynamics and Herglotz variational problem ⋮ Dirac structures in vakonomic mechanics ⋮ The Herglotz principle and vakonomic dynamics

Cites Work

• Isoholonomic problems and some applications
• Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
• Noether's theorem for singular Lagrangians
• Equivalence of dynamics for nonholonomic systems with transverse constraints
• Vakonomic mechanics versus non-holonomic mechanics: A unified geometrical approach
• On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints
• Symmetries and constants of the motion for singular Lagrangian systems
• Nonholonomic mechanical systems with symmetry
• Variational principles for constrained systems: Theory and experiment
• The geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems: The vakonomic bracket
• A complete classification of dynamical symmetries in classical mechanics
• Geometry of self-propulsion at low Reynolds number
• Toward a classification of dynamical symmetries in classical mechanics
• Abnormal Minimizers
• Optimal Control for Holonomic and Nonholonomic Mechanical Systems with Symmetry and Lagrangian Reduction
• Geometric Description of Vakonomic and Nonholonomic Dynamics. Comparison of Solutions
• REDUCTION OF PRESYMPLECTIC MANIFOLDS WITH SYMMETRY
• Geometric phases and robotic locomotion
• Law of Conservation of the Capital-Output Ratio
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item