Geometric Lagrangian approach to first-order systems and applications

DOI10.1063/1.527954zbMath0644.70012OpenAlexW2074250356MaRDI QIDQ3787544

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Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.527954

zbMATH Keywords

Hamiltonian formulationconstraint algorithmregular Lagrangianstheory of presymplectic systems

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Hamilton-Jacobi equations in mechanics (70H20) Lagrange's equations (70H03)

Related Items

Symmetries and constants of the motion for singular Lagrangian systems ⋮ The constraint algorithm in the jet formalism ⋮ The constraint algorithm for time-dependent Lagrangians ⋮ Invariants of Lagrangians and their classifications ⋮ Non-standard fractional Lagrangians ⋮ Higher order complex Lagrangian and Hamiltonian mechanics systems ⋮ Variational principles for nonpotential operators ⋮ Degenerate dynamical systems ⋮ Reduction of generalized Poisson and Nambu-Poisson manifolds ⋮ Skinner-Rusk approach to time-dependent mechanics

Cites Work

• Canonical variables for the Dirac theory
• Reduction of degenerate Lagrangian systems
• The time-evolution operator for singular Lagrangians
• Tangent bundle geometry Lagrangian dynamics
• First-order equivalent Lagrangians and conservation laws
• Geometric theory of the equivalence of Lagrangians for constrained systems
• Presymplectic manifolds and the Dirac–Bergmann theory of constraints
• On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics
• Equivalence between the Lagrangian and Hamiltonian formalism for constrained systems
• On the inverse problem of the calculus of variations