On the generalized Helmholtz conditions for Lagrangian systems with dissipative forces

In two recent papers necessary and sufficient conditions for a given system of second‐order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not independent and prove a stronger result accordingly. In two...

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Veröffentlicht in:	Zeitschrift für angewandte Mathematik und Mechanik 2010-06, Vol.90 (6), p.502-508
Hauptverfasser:	Crampin, M., Mestdag, T., Sarlet, W.
Format:	Artikel
Sprache:	eng
Schlagworte:	dissipative forces Exact sciences and technology Global analysis, analysis on manifolds Helmholtz conditions inverse problem Lagrangian systems Mathematics Numerical analysis Numerical analysis in abstract spaces Numerical analysis. Scientific computation Ordinary differential equations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Zusammenfassung:	In two recent papers necessary and sufficient conditions for a given system of second‐order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not independent and prove a stronger result accordingly. In two recent papers necessary and sufficient conditions for a given system of second‐order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. The authors point out that these conditions are not independent and prove a stronger result accordingly.
ISSN:	0044-2267 1521-4001
DOI:	10.1002/zamm.200900327