Computation in classical mechanics

American Journal of Physics

Volumn 76, Issue 4-5, 2008, Pages 334-339

  Timberlake, Todd ^a   Hasbun, Javier E ^b  

^a BERRY COLLEGE   (United States)

^b UNIVERSITY OF WEST GEORGIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 41849144148     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2870575     Document Type: Article

References (24)

1. John R. Taylor, Classical Mechanics (University Science Books, Sausalito, CA, 2005), Chap. 12.
2. Todd Timberlake, "A computational approach to teaching conservative chaos," Am. J. Phys. 72, 1002-1007 (2004).
3. Harvey Gould, Jan Tobochnik, and Wolfgang Christian, An Introduction to Computer Simulation Methods: Applications to Physical Systems (Addison-Wesley, New York, NY, 2007), 3rd ed., p. 75.
4. Alan Cromer, "Stable solutions using the Euler approximation," Am. J. Phys. 45, 455-459 (1981).
5. See for example, Ref. 3, pp. 45-46.
6. Louis N. Hand and Janet D. Finch, Analytical Mechanics (Cambridge U.P., Cambridge, 1998), pp. 202-204.
7. Algorithms that preserve phase space area, like the Euler-Cromer algorithm, are called symplectic algorithms (see Ref. 3, pp. 82-84). The Euler algorithm is not symplectic.
8. See for example, Ref. 3, p. 191.
9. See for example, Ref. 3, pp. 141-166.
10. This extraordinary initial speed is the muzzle velocity of the "Paris Gun" that was used by the German army to bombard Paris during World War I. See 〈www.daviddarling.info/encyclopedia/P/Paris_Gun.html〉 and 〈www.britannica.com/eb/article-9105701/Paris-Gun〉 for more details.
11. See 〈www.opensourcephysics.org〉 and Wolfgang Christian, Open Source Physics: A User's Guide with Examples (Pearson Addison-Wesley, San Francisco, CA, 2007).
12. Javier E. Hasbun, Classical Mechanics with MATLAB Applications (Jones and Bartlett, Sudbury, MA, 2008), Sec. 4.14.
13. MATLAB code is available upon request by e-mailing the author (J.H.). Open Source Physics applications not included in Ref. 12 will be made freely available at 〈www.westga.edu/-jhasbun/osp/osp.htm〉 in tandem with the textbook release.
14. MATHEMATICA code is available at 〈facultyweb.berry.edu/ttimberlake/ comp_phys/〉.
15. See Ref. 12 and 〈www.jbpub.com/catalog/0763746363/〉.
16. Stephen T. Thornton and Jerry B. Marion, Classical Dynamics of Particles and Systems (Thomson-Brooks/Cole, Belmont, CA, 2004), 5th ed.;
17. Grant R. Fowles and George L. Cassiday, Analytical Mechanics (Thomson-Brooks/Cole, Belmont, CA, 2005), 7th ed.
18. Rubin H. Landau and Manuel J. Paez, Computational Physics: Problem Solving with Computers (Wiley, New York, NY, 1997);
19. Steven E. Koonin and Dawn C. Meredith, Computational Physics: Fortran Version (Addison-Wesley, Reading, MA, 1990);
20. Samuel S. M. Wong, Computational Methods in Physics & Engineering (Prentice Hall, Englewood Cliffs, NJ, 1992);
21. Alejandro L. Garcia, Numerical Methods for Physics (Prentice Hall, Upper Saddle River, NJ, 2000), 2nd ed.;
22. Nicholas J. Giordano and Hisao Nakanishi, Computational Physics (Prentice Hall, Upper Saddle River, NJ, 2006), 2nd ed.;
23. Paul L. DeVries, A First Course in Computational Physics (Wiley, New York, NY, 1994);
24. David M. Cook, Computation and Problem Solving in Undergraduate Physics (Department of Physics, Lawrence University, Appleton, WI, 2003).