期刊
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY
卷 18, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1007/s11040-015-9196-3
关键词
Generalized Helmholtz conditions; Lagrangian systems; Non-conservative forces
资金
- Bilateral Cooperation Program [Ro-Hu 672/2013-2014]
In this paper we provide generalized Helmholtz conditions, in terms of a semi-basic 1-form, which characterize when a given system of second order ordinary differential equations is equivalent to the Lagrange equations, for some given arbitrary non-conservative forces. For the particular cases of dissipative or gyroscopic forces, these conditions, when expressed in terms of a multiplier matrix, reduce to those obtained in Mestdag et al. (Differential Geom. Appl. 29(1), 55-72, 2011). When the involved geometric structures are homogeneous with respect to the fibre coordinates, we show how one can further simplify the generalized Helmholtz conditions. We provide examples where the proposed generalized Helmholtz conditions, expressed in terms of a semi-basic 1-form, can be integrated and the corresponding Lagrangian and Lagrange equations can be found.
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