Hamiltonian Mechanics for Functionals Involving Second-Order Derivatives

[+] Author and Article Information
B. Tabarrok

Department of Mechanical Engineering, University of Victoria, British Columbia, V8W 3P6, Canada  

C. M. Leech

Department of Mechanical Engineering, UMIST, Manchester M60 1QD, UK

J. Appl. Mech 69(6), 749-754 (Oct 31, 2002) (6 pages) doi:10.1115/1.1505626 History: Received April 21, 2001; Revised February 28, 2002; Online October 31, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Lanczos, C., 1966, Variational Principles of Mechanics, 3rd Ed., University of Toronto Press, Toronto, pp. 229–243.
Goldstein, H., 1980, Classical Mechanics, 2nd Ed., Addison-Wesley, Reading, MA, pp. 438–457.
Whittaker, E. T., 1964, Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, Cambridge, UK.
Pars, L. A., 1965, A Treatise on Analytical Dynamics, Heinemann Educational Books, London, pp. 268–286.
Synge, J. L., 1960, Classical Dynamics in Encyclopedia of Physics, 3/1, S. Flügge, ed., Springer, Berlin, pp. 125–130.
Logan, J. D., 1977, Invariant Variational Principles, Academic Press, San Diego, CA, pp. 56–58.
Rund,  H., 1961, “The Theory of Problems in the Calculus of Variations Whose Lagrangian Function Involves Second-Order Derivatives: A New Approach,” Ann. Mat. Pure. Appl.,55, pp. 77–104.
Rund, H., 1966, The Hamilton-Jacobi Theory in the Calculus of Variations, Van Nostrand, New York.
Rodrigues,  P. R., 1976, “Géométrie Différentielle—Sur les Systèmes Méchaniques Généralisés,” C.R. Seances Acad. Sci., Ser. A, 282, pp. 1307–1309.
Tabarrok, B., and Rimrott, F. P. J., 1994, Variational Methods and Complementary Formulations in Dynamics, Kluwer, Dordrecht, The Netherlands.
Denman,  H. H., and Buch,  L. H., 1973, “Solution of the Hamilton-Jacobi Equation for Certain Dissipative Mechanical Systems,” J. Math. Phys., 14(3), pp 326–329.
Saletan, E. J., and Cromer, A. H., 1971, Theoretical Mechanics, John Wiley and Sons, New York, pp. 225–258.
Benton S. H., Jr., 1977, The Hamilton-Jacobi Equation: A Global Approach (Mathematics in Science and Engineering, Vol. 131), Academic Press, San Diego, CA, pp 8–13.
Sanz-Serna, J. M., and Calvo, M. P., 1994, Numerical Hamiltonian Problems (Applied Mathematics and Mathematical Computation 7), Chapman and Hall, London, pp. 129–153.
Leech,  C. M., and Tabarrok,  B., 1997, “Nonseparable Solutions to the Hamilton-Jacobi Equation,” ASME J. Appl. Mech., 64, pp. 636–641.
Leech,  C. M., 1997, “The Hamilton-Jacobi Equation applied to Continuum,” ASME J. Appl. Mech., 64, pp. 658–663.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In