Abstract
Among the problems C. D. Bailey has questioned in a recent paper (Ref. 1) are a precise and general formulation of Hamilton's variational principle and the establishment of a sufficiency criterion for this to be a minimum principle. In this paper, we will try to answer these questions using the geometric theory of classical mechanics.
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References
C. D. Bailey,Found. Phys. 11, 279 (1981).
F. Warner,Foundations of Differentiable Manifolds and Lie Groups (Scott and Foresman, Genview, Ill., 1971).
V. I. Arnold,Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
S. Kobayashi and K. Nomizu,Foundations of Differential Geometry (Interscience (Wiley), New York, 1963 and 1969), Volumes I and II.
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Yurtsever, U. Comments on “A more precise statement of Hamilton's principle”. Found Phys 13, 529–537 (1983). https://doi.org/10.1007/BF00729513
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DOI: https://doi.org/10.1007/BF00729513