Symmetries, constants of the motion, and reduction of mechanical systems with external forces

DOI10.1063/5.0045073zbMath1481.70067arXiv2101.09036OpenAlexW3148935073MaRDI QIDQ4987893

Manuel Lainz, Manuel de León, Asier López-Gordón

Publication date: 4 May 2021

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

Full work available at URL: https://arxiv.org/abs/2101.09036

zbMATH Keywords

reductionsymmetriesmomentum mapRayleigh dissipationHamiltonian systems with external forcesLagrangian systems with external forces

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (4)

Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds ⋮ Discrete Hamilton–Jacobi theory for systems with external forces ⋮ Geometric Hamilton–Jacobi theory for systems with external forces ⋮ Symmetries, Conservation and Dissipation in Time‐Dependent Contact Systems

Cites Work

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• The Noether theorems. Invariance and conservation laws in the twentieth century. Transl. from the French by Bertram E. Schwarzbach
• Extension of Noether's theorem to constrained non-conservative dynamical systems
• Reduction of symplectic manifolds with symmetry
• Noether's theory in classical nonconservative mechanics
• Momentum maps and Hamiltonian reduction
• A geometrical version of Noether's theorem in supermechanics
• Symmetries and constants of the motion for singular Lagrangian systems
• A summary on symmetries and conserved quantities of autonomous Hamiltonian systems
• Symmetries, conservation laws and multipliers via partial Lagrangians and Noether's theorem for classically non-variational problems
• Fluid Mechanics
• Reduction, symmetry, and phases in mechanics
• Symplectic approach to nonconservative mechanics
• Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces
• Hamiltonian dynamics with external forces and observations
• Discrete mechanics and variational integrators
• Rayleigh’s dissipation function at work
• Symmetries and constants of motion for constrained Lagrangian systems: a presymplectic version of the Noether theorem
• Symmetry theory and Lagrangian inverse problem for time-dependent second-order differential equations
• A complete classification of dynamical symmetries in classical mechanics
• Generalizations of Noether’s Theorem in Classical Mechanics
• Toward a classification of dynamical symmetries in classical mechanics
• Vector fields generating analysis for classical dissipative systems
• Invariant variation problems
• On the geometry of generalized Chaplygin systems
• Reduction of constrained systems with symmetries
• A new approach to the converse of Noether's theorem
• Symmetries and constants of the motion for higher-order Lagrangian systems
• Reduction and reconstruction of the dynamics of nonholonomic systems
• Almost complex structures induced in tangent bundles
• Symmetries, first integrals, and the inverse problem of Lagrangian mechanics. II

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