Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Essentials of Hamiltonian Dynamics
  • Cited by 11
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2012
Online ISBN:
9780511793721
DOI:
https://doi.org/10.1017/CBO9780511793721
Subjects:
Physics and Astronomy, General and Classical Physics, Nonlinear Science and Fluid Dynamics
Information

Book description

Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian treatments of classical mechanics. The book is well suited to a one-semester course, but is easily adapted to a more concentrated format of one-quarter or a trimester. A solutions manual and introduction to Mathematica® are available online at www.cambridge.org/Lowenstein.

Reviews

'This book provides a shortcut to many amazing and useful applications of this fascinating subject. I have no doubt that many instructors and students will benefit from this text.'

Anton Gorodetski Source: Physics Today

'… [this] book reminds us that the pursuit of science gives us the joy to wonder about and find answers to the mysteries of the universe, but also provides us with the tools needed to address future societal challenges … an excellent and inspiring read.'

Source: Physics Today

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
References
[1] H., Goldstein, C., Poole, and J. L., Safko, Classical Mechanics (3rd edn.), San Francisco, CA, Addison-Wesley, 2002
[2] E. T., Whittaker, A Treatise on Analytical Dynamics of Particles and Rigid Bodies, Cambridge, Cambridge University Press, 1988
[3] M., Abramowitz and I. A., Stegun, Handbook of Mathematical Functions, New York, Dover, 1965
[4] L. D., Landau and E. M., Lifshitz, Mechanics, Oxford, Pergamon Press, 1960
[5] J. L., Lagrange, Œuvres, vol. 6, Paris, 1873, pp. 272–292
[6] J., Liouville, J. Math. Pures Appl. 20 137–138 (1855)
[7] V. I., Arnol'd, Mathematical Methods of Classical Mechanics, New York, Springer-Verlag, 1978.
[8] V. I., Arnol'd, Ordinary Differential Equations, trans. R. A., Silverman, Cambridge, MA, MIT Press, 1973
[9] K., Efstathiou, M., Joyeux, and D. A., Sadovskii, Phys. Rev. A 69 032504 (2004)
[10] J. J., Duistermaat, Commun. Pure Appl. Math. 33, 687–706 (1980)
[11] A., Einstein, Verh. Deutsch. Phys. Ges. 19 82 (1917)
[12] L., Brillouin, J. Phys. Radium 7 353 (1926)
[13] J. B., Keller, Ann. Phys. (N.Y.) 4 180 (1958)
[14] J. B., Keller and S. I., Rubinow, Ann. Phys. (N.Y.) 9 24 (1960)
[15] R. H., Cushman and J. J., Duistermaat, J. Diff. Eqns. 172 42 (2001)
[16] M., Toda, Prog. Theor. Phys. Suppl. 45, 174 (1970)
[17] A. J., Lichtenberg and M. A., Lieberman, Regular and Chaotic Dynamics (2nd edn.), New York, Springer-Verlag, 1992
[18] M., Hénon, Phys. Rev. B 9 1921 (1974)
[19] W., Heisenberg, Z. Phys. 33 879 (1925)
[20] G. S., Ezra, K., Richter, G., Tanner, and D., Wintgen, J. Phys. B 24 L413 (1991)
[21] C. F. F., Karney and A., Bers, Phys. Rev. Lett. 39 550 (1977)
[22] G. D., Birkhoff, Dynamical Systems, New York, American Mathematical Society, 1927
[23] F., Gustavson, Astron. J. 71 670 (1966)
[24] M., Hénon and C., Heiles, Astron. J. 69 73 (1964)
[25] L. S., Hall, Physica D 8 90–116 (1983)
[26] A. N., Kolmogorov, Dokl. Akad. Nauk SSSR 98 527 (1954)
[27] J. K., Moser, Nach. Akad. Wiss. Göttingen II Math.-Phys. Kl.1 (1962)
[28] V. I., Arnol'd, Russ. Math. Surveys 18 No. 6, 85–191 (1963)
[29] J. V., José and E. J., Saletan, Classical Dynamics: a Contemporary Approach, Cambridge, Cambridge University Press, 1988
[30] V. I., Arnol'd, Sov. Math. Dokl. 2 247–249 (1960)
[31] A. M., Leontovich, Sov. Math. Dokl. 3 425–429 (1962)
[32] A., Celletti and L., Chierchia, KAM Stability and Celestial Mechanics, New York, American Mathematical Society, 2007
[33] G. M., Zaslavskii, R. Z., Sagdeev, D. A., Usikov, and A. A., Chernikov, Weak Chaos and Quasiregular Patterns, Cambridge, Cambridge University Press, 1991
[34] G. M., Zaslavsky, M., Edelman, and B. A., Niyazov, Chaos 7 159–181 (1997)
[35] G. M., Zaslavsky and B. A., Niyazov, Phys. Rep. 283 73–93 (1997)
[36] J., Wisdom, S. J., Peale, and F., Mignard, Icarus 58 137–152 (1984)
[37] J. J., Klavetter, Astron. J. 97 570–579 (1989)
[38] A. V., Devyatkin, D. L., Gorshanov, A. N., Gritsuk, A. V., Mel'nikov, M. Yu., Sidorov, and I. I., Shevchenko, Solar System Res. 36 248–259 (2002)
[39] V. V., Kouprianov and I. I., Shevchenko, Icarus 176 224–234 (2005)
[40] H., Dullin, A., Giacobbe, and R., Cushman, Physica D 190 15–37 (2004)
[41] R. H., Cushman, H. R., Dullin, A., Giacobbe, D. D., Holm, M., Joyeux, P., Lynch, D. A., Sadovskii, and B. I., Zhilinskii, Phys. Rev. Lett. 93 024302 (2004)
[42] M., Sanrey, M., Joyeux, and D. A., Sadovskii, J. Chem. Phys. 124 074318 (2006)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.