A new look at second-order equations and Lagrangian mechanics
- 11 July 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (10) , 1999-2009
- https://doi.org/10.1088/0305-4470/17/10/012
Abstract
To each second-order equation field Gamma on a tangent bundle TM, the authors associate a particular subset XGamma * of 1-forms on TM. Lagrangian systems then are characterised by the property that XGamma * contains an element which is non-degenerated and exact. For general second-order equation fields Gamma , they study type (1,1) tensor fields preserving both XGamma * and a kind of dual set of vector fields XGamma . Finally, they establish some theorems concerning Xgamma *, which cover known results in Lagrangian mechanics.Keywords
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