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Formal Foundation of Analytical Dynamics Based on the Contact Structure

Published online by Cambridge University Press:  22 January 2016

Minoru Kurita
Minoru Kurita*
Affiliation:
Mathematical Institute, Nagoya University
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A systematic treatment of analytical dynamics was given by E. Cartan in [1], where the 1-form plays the fundamental role. We give here a further investigation. One of our main purposes is to clarify relations between dynamical systems and Finsler spaces and the other is to formulate an intrinsic bundle structure of the systems. This paper is closely related to my previous papers [4] [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 107 - 119
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Cartarn, E., Leçons sur les invariants intégraux. Hermann Fils, Paris. 1922.Google Scholar
[2] Caratheodory, C., Variationsrechnung und partielle Differentialgleichungen erster Ordnung. B.G. Teubner, Leibzig und Berlin. 1935.Google Scholar
[3] Caratheodory, C., Geometrische Optik. Verlag von Julius Springer, Berlin. 1937.Google Scholar
[4] Kurita, M., On the dilatation in Finsler spaces. Osaka Math. J., 15 (1963), 87–97.Google Scholar
[5] Kurita, M., Theory of Finsler spaces based on the contact structure. J. Math. Soc. Japan, 18 (1966), 119–134.Google Scholar