Second‐order equation fields and the inverse problem of Lagrangian dynamics
- 1 December 1987
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 28 (12) , 2851-2857
- https://doi.org/10.1063/1.527683
Abstract
The transformation properties of determined, autonomous systems of second‐order ordinary differential equations, identified as vector fields on the tangent bundle of the space of dependent variables, are derived and studied. The inverse problem of Lagrangian dynamics is studied from this transformation viewpoint as well as the problem of alternative Lagrangians. In particular, regular Lagrangians which are analytic as functions of the first derivatives are considered. Finally, the inverse problem for second‐order systems corresponding to the geodesic flow of a symmetric linear connection is investigated.Keywords
This publication has 9 references indexed in Scilit:
- Symmetries of nonlinear differential equations and linearisationJournal of Physics A: General Physics, 1987
- Killing tensors in spaces of constant curvatureJournal of Mathematical Physics, 1986
- Affine bundles and integrable almost tangent structuresMathematical Proceedings of the Cambridge Philosophical Society, 1985
- Tangent bundle geometry Lagrangian dynamicsJournal of Physics A: General Physics, 1983
- Lagrangians for spherically symmetric potentialsJournal of Mathematical Physics, 1982
- The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamicsJournal of Physics A: General Physics, 1982
- On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamicsJournal of Physics A: General Physics, 1981
- Killing tensors and the separation of the Hamilton-Jacobi equationCommunications in Mathematical Physics, 1975
- Espaces variationnels et mécaniqueAnnales de l'institut Fourier, 1962