Abstract
Mechanics is a branch of physics studying motion. The history of mechanics, as well as the history of other branches of science, is a history of attempts to explain the world by means of the smallest possible number of universal laws and general principles. The most successful and fruitful attempts stem from the idea that the observable events are extreme in their character and that the general principles sought are variational, i.e. they assert that certain parameters obtain their maximum or minimum values in realizable physical processes.
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References
V.I. Arnold. Mathematical methods of classical mechanics. Springer-Verlag, Berlin, 1989.
V.I. Arnold, V.V. Kozlov, and A.I. Neistadt. Mathematical aspects of classical and celestial mechanics, volume 3 of Encycl. of Math. Sciences. Springer, 1988.
H.H. Goldstine. A history of the calculus of variations from the 17th through the 19th century. Springer-Verlag, Berlin, 1980.
F. Klein. Vorlesungen uber die Entwicklung der Mathematik. Verlag von Julius Springer, Berlin, 1927.
C. Lanczos. The variational principles of mechanics. University of Toronto Press, Toronto, 1962.
L.D. Landau and E.M. Lifshits. Mechanics. Pergamon Press, Oxford, New York, 1976.
A.J. Lichtenberg and M.A. Liberman. Regular and chaotic dynamics. Springer-Verlag, Berlin, 1992.
E. Mach. The science of mechanics. Open Court Publishing Company, La Salle, I., London, 5th edition, 1942.
A. Mayer. Geschichte des Princips der Kleinsten Aktion. Leipzig, 1877.
L.S. Polak, editor. Variational principles of mechanics. Fizmatgiz, Moscow, 1959.
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Berdichevsky, V. (2009). Variational Principles. In: Variational Principles of Continuum Mechanics. Interaction of Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88467-5_1
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DOI: https://doi.org/10.1007/978-3-540-88467-5_1
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