Abstract
Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space. If we parametrize the path between points P and Q by ϑ, then Jacobi’s principle states:
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© 2001 Springer-Verlag Berlin Heidelberg
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Dittrich, W., Reutera, M. (2001). Jacobi Fields, Conjugate Points. In: Classical and Quantum Dynamics. Advanced Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56430-7_5
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DOI: https://doi.org/10.1007/978-3-642-56430-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42066-8
Online ISBN: 978-3-642-56430-7
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