A computational approach to teaching conservative chaos

American Journal of Physics

Volumn 72, Issue 8, 2004, Pages 1002-1007

  Timberlake, Todd ^a  

^a BERRY COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344572332     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1764559     Document Type: Article

References (16)

1. Linda E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, New York, 1992).
2. Charles H. Patterson, "Two approaches to teaching computational physics," Comput. Sci. Eng. 4(6), 64-68 (2002).
3. Todd Timberlake, Justin Harvey, Matt Lewis, and Wesley Taylor, "Beyond the standard map: A numerical investigation of indifferent fixed points" (unpublished).
4. Harvey Gould, "Computational physics and the undergraduate curriculum," Comput. Phys. Commun. 127, 6-10 (2000).
5. Robert L. Zimmerman and Fredrick I. Olness, Mathematica For Physics (Addison Wesley, San Francisco, 2002); Patrick T. Tam, A Physicist's Guide to Mathematica (Academic Press, San Diego, 1997); Marvin L. De Jong, Mathematica for Calculus-Based Physics (Addison-Wesley, San Francisco, 1999); Ronald Greene, Classical Mechanics With Maple (Springer-Verlag, New York, 1995).
6. Robert L. Zimmerman and Fredrick I. Olness, Mathematica For Physics (Addison Wesley, San Francisco, 2002); Patrick T. Tam, A Physicist's Guide to Mathematica (Academic Press, San Diego, 1997); Marvin L. De Jong, Mathematica for Calculus-Based Physics (Addison-Wesley, San Francisco, 1999); Ronald Greene, Classical Mechanics With Maple (Springer-Verlag, New York, 1995).
7. Robert L. Zimmerman and Fredrick I. Olness, Mathematica For Physics (Addison Wesley, San Francisco, 2002); Patrick T. Tam, A Physicist's Guide to Mathematica (Academic Press, San Diego, 1997); Marvin L. De Jong, Mathematica for Calculus-Based Physics (Addison-Wesley, San Francisco, 1999); Ronald Greene, Classical Mechanics With Maple (Springer-Verlag, New York, 1995).
8. Robert L. Zimmerman and Fredrick I. Olness, Mathematica For Physics (Addison Wesley, San Francisco, 2002); Patrick T. Tam, A Physicist's Guide to Mathematica (Academic Press, San Diego, 1997); Marvin L. De Jong, Mathematica for Calculus-Based Physics (Addison-Wesley, San Francisco, 1999); Ronald Greene, Classical Mechanics With Maple (Springer-Verlag, New York, 1995).
9. Robert C. Hilborn, Chaos and Nonlinear Dynamics, 2nd ed. (Oxford University Press, Oxford, U.K., 2000).
10. Louis N. Hand and Janet D. Finch, Analytical Mechanics (Cambridge University Press, Cambridge, U.K., 1998).
11. Michael Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989).
12. See EPAPS Document No. E-AJPIAS-72-011408 for a Mathematica notebook containing the code used to produce the figures in this article which can be found at (http://fsweb.berry.edu/academic/mans/ttimberlake/cc/). Other materials related to teaching Hamiltonian chaos, including lecture slides and examples of student work, can also be found at this site. A direct link to this document may be found in the online article's HTML reference section. The document may also be reached via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps. See the EPAPS homepage for more information.
13. Boris V. Chirikov, "A universal instability of many dimensional oscillator systems," Phys. Rep. 52, 263-379 (1979).
14. Louis N. Hand and Janet D. Finch, Analytical Mechanics (Cambridge University Press, Cambridge, U.K., 1998), pp. 433-436.
15. All of the animations mentioned in the article can be found at the website mentioned in Ref. 9.
16. Louis N. Hand and Janet D. Finch, Analytical Mechanics (Cambridge University Press, Cambridge, U.K., 1998), pp. 439-442.