Equivalent Lagrangians: Multidimensional case
- 1 July 1981
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (7) , 1414-1419
- https://doi.org/10.1063/1.525062
Abstract
We generalize a theorem known for one-dimensional nonsingular equivalent Lagrangians (L and ?) to the multidimensional case. In particular, we prove that the matrix Λ, which relates the left-hand sides of the Euler–Lagrange equations obtained from L and ?, is such that the trace of all its integer powers are constants of the motion. We construct several multidimensional examples in which the elements of Λ are functions of position, velocity, and time, and prove that in some cases equivalence prevails even if detΛ = 0.Keywords
This publication has 7 references indexed in Scilit:
- Ambiguities in the Lagrangian and Hamiltonian formalism: Transformation propertiesIl Nuovo Cimento B (1971-1996), 1977
- Necessary and sufficient conditions for the existence of a Lagrangian in field theory. III. Generalized analytic representations of tensorial field equationsAnnals of Physics, 1977
- Necessary and sufficient conditions for the existence of a Lagrangian in field theory II. Direct analytic representations of tensorial field equationsAnnals of Physics, 1977
- Necessary and sufficient conditions for the existence of a Lagrangian in field theory. I. Variational approach to self-adjointness for tensorial field equationsAnnals of Physics, 1977
- Canonical transformations and quadratic hamiltoniansIl Nuovo Cimento B (1971-1996), 1972
- q-Equivalent Particle Hamiltonians. I. The Classical One-Dimensional CaseJournal of Mathematical Physics, 1966
- Solution of the inverse problem of the calculus of variationsTransactions of the American Mathematical Society, 1941