Equivalent Lagrangians: Multidimensional case

S. Hojman, H. Harleston

Research output: Contribution to journalArticlepeer-review

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We generalize a theorem known for one-dimensional nonsingular equivalent Lagrangians (L and L) 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 L, 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.

Original languageEnglish
Pages (from-to)1414-1419
Number of pages6
JournalJournal of Mathematical Physics
Issue number7
StatePublished - 1980


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