Second-order equation fields and the inverse problem of Lagrangian dynamics

DOI10.1063/1.527683zbMath0638.70013OpenAlexW2012242286MaRDI QIDQ3779806

Gerard Thompson

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1063/1.527683

zbMATH Keywords

transformation propertiestangent bundlevector fieldsinverse problem of Lagrangian dynamicsdetermined, autonomous systems of second-order ordinary differential equationsgeodesic flow of a symmetric linear connection

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lagrange's equations (70H03)

Related Items (4)

Linearization of second order ordinary differential equations via Cartan's equivalence method ⋮ Geometric characterization of linearisable second-order differential equations ⋮ The inverse problem in the calculus of variations and the geometry of the tangent bundle ⋮ Variational principles for nonpotential operators

Cites Work

• Killing tensors and the separation of the Hamilton-Jacobi equation
• Espaces variationnels et mécanique
• Symmetries of nonlinear differential equations and linearisation
• Tangent bundle geometry Lagrangian dynamics
• The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
• Affine bundles and integrable almost tangent structures
• Killing tensors in spaces of constant curvature
• On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics
• Lagrangians for spherically symmetric potentials

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