The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
- 1 May 1982
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 15 (5) , 1503-1517
- https://doi.org/10.1088/0305-4470/15/5/013
Abstract
Deals with the general problem of finding a multiplier matrix that can give to a prescribed system of second-order ordinary equations the structure of Euler-Lagrange equations. The approach is based on a generalisation of previous studies on linear systems. The main result concerns a set of necessary and sufficient conditions for the existence of a multiplier, which contains an infinite set of algebraic equations, the coefficients of which can be used to derive necessary conditions involving only the given right-hand sides of the differential equations. An outline is given of interesting points for future studies, and an example is presented for which all multipliers are explicitly constructed.Keywords
This publication has 11 references indexed in Scilit:
- Time-dependent linear systems derivable from a variational principleInternational Journal of Engineering Science, 1982
- On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamicsJournal of Physics A: General Physics, 1981
- Symmetries, first integrals and the inverse problem of Lagrangian mechanicsJournal of Physics A: General Physics, 1981
- Equivalent Lagrangians: Multidimensional caseJournal of Mathematical Physics, 1981
- Origin of non-Noether invariantsPhysics Letters A, 1979
- Criteria for partial differential equations to be Euler-Lagrange equationsJournal of Differential Equations, 1977
- q-Equivalent Particle Hamiltonians. I. The Classical One-Dimensional CaseJournal of Mathematical Physics, 1966
- The range of application of the lagrange formalism — IIl Nuovo Cimento (1869-1876), 1957
- Solution of the inverse problem of the calculus of variationsTransactions of the American Mathematical Society, 1941
- Ueber die physikalische Bedeutung des Prinicips der kleinsten Wirkung.Journal für die reine und angewandte Mathematik (Crelles Journal), 1887