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Second-order equation fields and the inverse problem of Lagrangian dynamics. (English) Zbl 0638.70013
The transformation properties of determined, autonomous systems of second-order ordinary differential equations, identified as vector fields on the tangent bundle of the space of dependent variables, are defined and studied. The inverse problem of Lagrangian dynamics is studied from this transformation viewpoint as well as the problem of alternative Lagrangians. In particular, regular Lagrangians which are analytic as functions of the first derivatives are considered. Finally, the inverse problem for second-order systems corresponding to the geodesic flow of a symmetric linear connection is investigated.

MSC:
70H03 Lagrange’s equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37C10 Dynamics induced by flows and semiflows
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References:
[1] DOI: 10.1088/0305-4470/14/10/012 · Zbl 0475.70022
[2] DOI: 10.1088/0305-4470/15/5/013 · Zbl 0537.70018
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