The inverse problem for Lagrangian systems with certain non-conservative forces |
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Authors: | T. Mestdag W. Sarlet M. Crampin |
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Affiliation: | a Department of Mathematics, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium b Department of Mathematics and Statistics, La Trobe University, Bundoora, Victoria 3086, Australia |
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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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Keywords: | 70H03 70F17 49N45 |
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