Phase space methods and the Hamilton-Jacobi form of dynamics

  • N. Mukunda


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.


Classical dynamics phase-space method Hamilton-Jacobi theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Born M 1927The Mechanics of the Atom (London: G. Bell and Sons), Ch. 1MATHGoogle Scholar
  2. [2]
    Brillouin L 1926 Comptes Rendus183 24Google Scholar
  3. [3]
    Caratheodory C 1965Calculus of Variations and Partial Differential Equations of the First Order Part I (San Francisco, California: Holden-Day)MATHGoogle Scholar
  4. [4]
    Dirac P A M 1951Can. J. Math. 3 1MATHMathSciNetGoogle Scholar
  5. [5]
    Einstein A 1917Verh. d. Deut. Phys. Ges. 19 82Google Scholar
  6. [6]
    Epstein P 1916Phys. Zeitschr. 17 148Google Scholar
  7. [7]
    Kramers H A 1926Z. Phys. 39 828CrossRefGoogle Scholar
  8. [8]
    Lanczos C 1949The Variational Principles of Mechanics (Toronto: University of Toronto Press) Ch. VIIIMATHGoogle Scholar
  9. [9]
    Noether E 1918 Nachr. Ges. Wiss. Gött. 37Google Scholar
  10. [10]
    Nordheim L and Fues E 1927Die Hamilton-Jacobische Theorie der Dynamik Geiger—Scheel Handbuch der Physik Vol. V (Berlin: Springer) pp. 91–130Google Scholar
  11. [11]
    Rund H 1966The Hamilton-Jacobi Theory in the Calculus of Variations (London: D. Van Nostrand Co.)MATHGoogle Scholar
  12. [12]
    Saletan E J and Cromer A H 1971Theoretical Mechanics (New York: John Wiley) Ch. IXMATHGoogle Scholar
  13. [13]
    Schrödinger E 1926Ann. Phys. 79 361, 489; reprinted in Ludwig G 1968Wave Mechanics (Oxford: Pergamon Press)CrossRefGoogle Scholar
  14. [14]
    Sommerfeld A 1916Ann. Phys. 51 1CrossRefMathSciNetGoogle Scholar
  15. [15]
    Sommerfeld A 1934Atomic Structure and Spectral Lines 3rd ed. (London: Methuen and Co.) Vol. 1 § 6Google Scholar
  16. [16]
    Sudarshan E C G and Mukunda N 1974Classical Dynamics—A Modern Perspective (New York: John Wiley)MATHGoogle Scholar
  17. [17]
    Wentzel G 1926Z. Phys. 38 518CrossRefGoogle Scholar
  18. [18]
    Whittaker E T 1927A Treatise on the Analytical Dynamics of Particles and Rigid Bodies 3rd ed. (Cambridge: University Press) Ch. XI, XIIMATHGoogle Scholar
  19. [19]
    Wilson W 1915Phil. Mag. 29 795Google Scholar

Copyright information

© Indian Academy of Sciences 1978

Authors and Affiliations

  • N. Mukunda
    • 1
  1. 1.Centre for Theoretical StudiesIndian Institute of ScienceBangaloreIndia

Personalised recommendations