The inverse problem for Lagrangian systems with certain non-conservative forces
| Autor: | Tom Mestdag, Willy Sarlet, Michael Crampin |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Mathematics - Differential Geometry
Gyroscopic forces Helmholtz conditions FOS: Physical sciences Mathematical Physics (math-ph) 70H03 70F17 49N45 Inverse problem Dissipation Type (model theory) Mechanical system Multiplier (Fourier analysis) Matrix (mathematics) Differential Geometry (math.DG) Computational Theory and Mathematics Lagrangian systems FOS: Mathematics Applied mathematics Dissipative forces Geometry and Topology Representation (mathematics) Conservative force Mathematical Physics Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 29:55-72 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2010.11.002 |
| Popis: | 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. 28 pages |
| Databáze: | OpenAIRE |
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