Contact Hamiltonian and Lagrangian systems with nonholonomic constraints

DOI10.3934/jgm.2021001zbMath1496.37071arXiv1911.05409OpenAlexW3115907445MaRDI QIDQ2052470

Manuel de León, Manuel Lainz, Víctor Manuel Jiménez

Publication date: 26 November 2021

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.05409

zbMATH Keywords

dissipative systemsnonholonomic constraintsnonholonomic mechanicscontact Hamiltonian systemsHerglotz principleJacobi nonholonomic bracket

Mathematics Subject Classification ID

Contact manifolds (general theory) (53D10) Nonholonomic systems related to the dynamics of a system of particles (70F25) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Nonholonomic dynamical systems (37J60) Contact systems (37J55)

Related Items

Symplectic and inverse spectral geometry of integrable systems: a glimpse and open problems ⋮ Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems ⋮ Time-dependent contact mechanics ⋮ Lagrangian-Hamiltonian formalism for cocontact systems ⋮ Contact Lie systems: theory and applications ⋮ Constrained Lagrangian dissipative contact dynamics ⋮ Hamiltonian systems on almost cosymplectic manifolds ⋮ Contact Lagrangian systems subject to impulsive constraints ⋮ The Herglotz principle and vakonomic dynamics ⋮ A geometric approach to contact Hamiltonians and contact Hamilton–Jacobi theory

Cites Work

• A Lagrangian variational formulation for nonequilibrium thermodynamics. I: Discrete systems.
• Nonlinear dynamics and stability of the skateboard
• On the motion of Chaplygin's sledge
• Reduction of some classical non-holonomic systems with symmetry
• Les variétés de Jacobi et leurs algèbres de Lie associees
• Lectures on the geometry of Poisson manifolds
• Nonholonomic reduction
• Contact Hamiltonian dynamics: Variational principles, invariants, completeness and periodic behavior
• On the history of the development of the nonholonomic dynamics
• On the integration theory of equations of nonholonomic mechanics
• A historical review on nonholomic mechanics
• A contact geometry framework for field theories with dissipation
• On the geometry of discrete contact mechanics
• Infinitesimal symmetries in contact Hamiltonian systems
• Nonholonomic mechanical systems with symmetry
• LOCAL LIE ALGEBRAS
• A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
• The Variational Principle of Hergloz and Related Results
• Non-holonomic Lagrangian systems in jet manifolds
• Generalized variational principle of Herglotz for several independent variables. First Noether-type theorem
• Contact geometry for simple thermodynamical systems with friction
• Contact Hamiltonian systems
• Contact geometry and thermodynamics
• On the geometry of non-holonomic Lagrangian systems
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• Contact variational integrators
• On Hamilton's principle for nonholonomic systems
• Higher-order mechanical systems with constraints
• From variational to bracket formulations in nonequilibrium thermodynamics of simple systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item