Abstract
A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.
Similar content being viewed by others
References
Born M 1927The Mechanics of the Atom (London: G. Bell and Sons), Ch. 1
Brillouin L 1926 Comptes Rendus183 24
Caratheodory C 1965Calculus of Variations and Partial Differential Equations of the First Order Part I (San Francisco, California: Holden-Day)
Dirac P A M 1951Can. J. Math. 3 1
Einstein A 1917Verh. d. Deut. Phys. Ges. 19 82
Epstein P 1916Phys. Zeitschr. 17 148
Kramers H A 1926Z. Phys. 39 828
Lanczos C 1949The Variational Principles of Mechanics (Toronto: University of Toronto Press) Ch. VIII
Noether E 1918 Nachr. Ges. Wiss. Gött. 37
Nordheim L and Fues E 1927Die Hamilton-Jacobische Theorie der Dynamik Geiger—Scheel Handbuch der Physik Vol. V (Berlin: Springer) pp. 91–130
Rund H 1966The Hamilton-Jacobi Theory in the Calculus of Variations (London: D. Van Nostrand Co.)
Saletan E J and Cromer A H 1971Theoretical Mechanics (New York: John Wiley) Ch. IX
Schrödinger E 1926Ann. Phys. 79 361, 489; reprinted in Ludwig G 1968Wave Mechanics (Oxford: Pergamon Press)
Sommerfeld A 1916Ann. Phys. 51 1
Sommerfeld A 1934Atomic Structure and Spectral Lines 3rd ed. (London: Methuen and Co.) Vol. 1 § 6
Sudarshan E C G and Mukunda N 1974Classical Dynamics—A Modern Perspective (New York: John Wiley)
Wentzel G 1926Z. Phys. 38 518
Whittaker E T 1927A Treatise on the Analytical Dynamics of Particles and Rigid Bodies 3rd ed. (Cambridge: University Press) Ch. XI, XII
Wilson W 1915Phil. Mag. 29 795
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mukunda, N. Phase space methods and the Hamilton-Jacobi form of dynamics. Proc. Indian Acad. Sci. (Math. Sci.) 87, 85–105 (1978). https://doi.org/10.1007/BF02837704
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02837704