The Herglotz principle and vakonomic dynamics

DOI10.1007/978-3-030-80209-7_21zbMath1500.37043arXiv2106.02404OpenAlexW3183743531MaRDI QIDQ2117848

Manuel de León, Manuel Lainz, Miguel C. Muñoz-Lecanda

Publication date: 22 March 2022

Full work available at URL: https://arxiv.org/abs/2106.02404

zbMATH Keywords

optimal controlvakonomic dynamicsconstrained systemscontact Hamiltonian systems

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15) Dynamical systems in control (37N35) Contact manifolds (general theory) (53D10) Constrained dynamics, Dirac's theory of constraints (70H45) Other variational principles in mechanics (70H30) Almost contact and almost symplectic manifolds (53D15) Nonholonomic dynamical systems (37J60) Contact systems (37J55)

Related Items (4)

Nonautonomous k-contact field theories ⋮ Lagrangian-Hamiltonian formalism for cocontact systems ⋮ A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian ⋮ Constrained Lagrangian dissipative contact dynamics

Cites Work

• Contact structure in thermodynamic theory
• Manifolds, tensor analysis, and applications.
• Some geometric aspects of variational calculus in constrained systems
• A contact geometry framework for field theories with dissipation
• On the geometry of discrete contact mechanics
• Contact Hamiltonian and Lagrangian systems with nonholonomic constraints
• Infinitesimal symmetries in contact Hamiltonian systems
• Discrete vakonomic mechanics
• Geometric Description of Vakonomic and Nonholonomic Dynamics. Comparison of Solutions
• Generalized variational principle of Herglotz for several independent variables. First Noether-type theorem
• Contact variational integrators
• Symmetries in vakonomic dynamics: Applications to optimal control
• Singular Lagrangians and precontact Hamiltonian systems

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