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arXiv · 1004.0674

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

T. Mestdag·W. Sarlet·M. Crampin
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Abstract

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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T. Mestdag, W. Sarlet, M. Crampin. 2010-04-05. The inverse problem for Lagrangian systems with certain non-conservative forces. https://doi.org/10.1016/j.difgeo.2010.11.002

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