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Finslerian approach to Lagrange mechanics. (English) Zbl 0789.53013
Szenthe, J. (ed.) et al., Differential geometry and its applications. Proceedings of a colloquium, held in Eger, Hungary, August 20-25, 1989, organized by the János Bolyai Mathematical Society. Amsterdam: North- Holland Publishing Company. Colloq. Math. Soc. János Bolyai. 56, 411-415 (1992).
Let \(M^ n = (M,g_{ij}(x,y))\) be a generalized Lagrange space with the \(d\)-tensor field \(g_{ij} = \gamma_{ij}(x) + y_ iy_ j/c^ 2\), where \(\gamma_{ij}\) is a Riemannian metric, \(c\) a positive nuber, \((x^ i,y^ i)\) a canonical coordinate system of \(TM\) and \(y_ i = \gamma_{ij}y^ j\). The purpose of the present paper is to make an abstract of the main results on \(M^ n\) from two joint papers with R. Miron [Tensor, New Ser. 48, 52-63 and 153-168 (1989; Zbl 0703.53021 and Zbl 0708.53057)].
For the entire collection see [Zbl 0764.00002].
MSC:
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
Keywords:
Lagrange space
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