Abstract
We define the notion of higher order Lagrangian and the notion of integral of action. We investigate the variational problem for autonomous Lagrangians deriving the Euler-Lagrange equations. The notion of Lagrange space of order k is introduced by means of regular nondegenerate Lagrangian defined on the total space of the k-accelerations bundle T k M. In this case the Craig-Synge equations determine a k-semispray, which depend only on the considered Lagrangian. Therefore the geometry of the Lagrange space of order k is based on the mentioned k-semispray, [94].
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© 2003 Springer Science+Business Media Dordrecht
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Miron, R. (2003). Lagrange Spaces of Higher Order. In: The Geometry of Higher-Order Hamilton Spaces. Fundamental Theories of Physics, vol 132. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0070-3_2
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DOI: https://doi.org/10.1007/978-94-010-0070-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3995-6
Online ISBN: 978-94-010-0070-3
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