On the many-time formulation of classical particle dynamics

DOI10.1063/1.528224zbMath0678.70001OpenAlexW2145384233MaRDI QIDQ3835060

G. Longhi, Josep M. Pons, Luca Lusanna

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1063/1.528224

zbMATH Keywords

variational principleinvariance groupNoether theoremconstraintscoisotropic imbeddingsLie-König theoremn-time equations of motionnonrelativistic no-interaction theoremone-time dynamics of n nonrelativistic particlespresymplectic stuctures

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Axiomatics, foundations (70A05)

Related Items (9)

Centers of mass and rotational kinematics for the relativistic N-body problem in the rest-frame instant form ⋮ On the BRS’s ⋮ Extension of many-time Hamiltonian formalism to the theory of deformable bodies ⋮ Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamics ⋮ Lagrangian and Hamiltonian many-time equations ⋮ The rest-frame instant form of metric gravity. ⋮ QUANTUM MECHANICS IN NONINERTIAL FRAMES WITH A MULTITEMPORAL QUANTIZATION SCHEME II: NONRELATIVISTIC PARTICLES ⋮ THE CHRONO-GEOMETRICAL STRUCTURE OF SPECIAL AND GENERAL RELATIVITY: A RE-VISITATION OF CANONICAL GEOMETRODYNAMICS ⋮ Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics

Cites Work

• Inverse problem in classical mechanics: Dissipative systems
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• The problem of physical coordinates in predictive Hamiltonian systems
• Elementary Relativistic Wave Mechanics of Spin 0 and Spin 1/2 Particles
• Observables in General Relativity
• The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
• A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
• Generalizations of Noether’s Theorem in Classical Mechanics
• Symmetries, first integrals and the inverse problem of Lagrangian mechanics
• Lagrangians for spherically symmetric potentials
• Unique Canonical Representation of the Inhomogeneous Lorentz Group in Relativistic Particle Dynamics
• A General Survey of the Theory of the Bethe-Salpeter Equation
• Forms of Relativistic Dynamics
• On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
• Dirac Bracket Transformations in Phase Space

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