Evading the inverse problem for second-order ordinary differential equations by using additional variables
- 1 February 1987
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 3 (1) , 51-63
- https://doi.org/10.1088/0266-5611/3/1/010
Abstract
Caviglia (1986) has recently recalled that any system of second-order ordinary differential equations may be extended in such a way as to embed them in a system of Euler-Lagrange equations. The authors give a geometrical description of this construction and show how in effect the same function may be used to define both a hamiltonian and a lagrangian extension of the given system. They further clarify the way in which the linear variational equations and their adjoints come into the picture, and also their connection with symmetries of the system and invariant 1-forms.Keywords
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