A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
M Crampin; G E Prince; G Thompson; M Crampin; Faculty of Maths., Open Univ., Milton Keynes, UK; G E Prince; Faculty of Maths., Open Univ., Milton Keynes, UK; G Thompson; Faculty of Maths., Open Univ., Milton Keynes, UK
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1984-05-11
Аннотация:
Appropriate geometrical machinery for the study of time-dependent Lagrangian dynamics is developed. It is applied to the inverse problem of the calculus of variations, and a set of necessary and sufficient conditions for the existence of a Lagrangian are given, in terms of the existence of a 2-form with suitable properties, which are exactly equivalent to the Helmholtz conditions.
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