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The Euler‐Maupertuis principle of least action as variational inequality
Author(s) -
Leine R. I.,
Aeberhard U.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700666
Subject(s) - action (physics) , principle of least action , variational principle , mathematics , euler's formula , context (archaeology) , variational inequality , hamilton's principle , mathematical analysis , classical mechanics , physics , quantum mechanics , equations of motion , paleontology , biology
Starting from Hamilton's Principle, the current paper discusses how we can derive the Euler‐Maupertuis Principle of Least Action in the context of non‐smooth dynamics. This variational principle allows us to directly obtain the space curve y ( x ) of a point‐mass in a potential field V ( x , y ) without referring to the temporal dynamics. This paper generalises the Euler‐Maupertuis Principle of Least Action to systems with impact by formulating the principle as a variational inequality. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)