The inverse problem for Lagrangian systems with certain non-conservative forces

Details The inverse problem for Lagrangian systems with certain non-conservative forces The inverse problem for Lagrangian systems with certain non-conservative forces

2010-04-05

arxiv.org/abs/1004.0674v1

Diff Geom Appl 29 (2011) 55 - 72

Mathematics

Differential Geometry

28 pages

Scientific paper

10.1016/j.difgeo.2010.11.002

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic forces. Our approach focusses primarily on obtaining coordinate-free conditions for the existence of a suitable non-singular multiplier matrix, which will lead to an equivalent representation of a given system of second-order equations as one of these Lagrangian systems with non-conservative forces.

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