Applications of the Mathieu equation

American Journal of Physics

Volumn 64, Issue 1, 1996, Pages 39-44

  Ruby, Lawrence ^a  

^a OREGON HEALTH AND SCIENCE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030558389     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18290     Document Type: Article

References (16)

1. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Part 1, Sec. 5.2.
2. J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1965), Sec. 7-5. See also L. Ruby, "Answer to Question #4 ['Is there a physics application that is best analyzed in terms of continued fractions'.',' Dwight E. Neuenschwander, Am. J. Phys. 62(10), 871(1994)]," Am. J. Phys. 63, 14-15 (1995).
3. J. Mathews and R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1965), Sec. 7-5. See also L. Ruby, "Answer to Question #4 ['Is there a physics application that is best analyzed in terms of continued fractions'.',' Dwight E. Neuenschwander, Am. J. Phys. 62(10), 871(1994)]," Am. J. Phys. 63, 14-15 (1995).
4. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, U.S. Govt. Printing Office, 1964 (reprinted by Dover, New York, 1965), Chap. 20. A more extensive treatment with the same notation is by N. W. McLachlan, Theory of Application of Mathieu Functions (Oxford U. P., Oxford, 1947) (reprinted by Dover, New York, 1964).
5. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, U.S. Govt. Printing Office, 1964 (reprinted by Dover, New York, 1965), Chap. 20. A more extensive treatment with the same notation is by N. W. McLachlan, Theory of Application of Mathieu Functions (Oxford U. P., Oxford, 1947) (reprinted by Dover, New York, 1964).
6. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Sec. 1.18.
7. F. M. Phelps III and J. H. Hunter, Jr., "An analytical solution of the inverted pendulum," Am. J. Phys. 33, 285-295 (1965).
8. L. Blitzer, "Inverted pendulum," Am. J. Phys. 33, 1076-1078 (1965).
9. F. M. Phelps III and J. H. Hunter, Jr., Note: "Reply to Joshi's Comments on a Damping Term in the Equations of Motion of the Inverted Pendulum," Am. J. Phys. 34, 533-535 (1966).
10. S. Humphries, Jr., Principles of Charged Particle Acceleration (Wiley, New York, 1956), Sec. 14.6.
11. A. Allievi and A. Soudack, "Ship stability via the Mathieu equation," Int. J. Control 51, 139-167 (1990).
12. Reference 8, Sec. 15.3.
13. E. L. Kelly et al.., "Two electron models of a constant-frequency relativistic cyclotron," Rev. Sci. Instrum. 27, 493-503 (1956).
14. H. Winter and H. W. Ortjohann, "Simple demonstration of storing macroscopic particles in a 'Paul trap,'" Am. J. Phys. 59, 807-813 (1991).
15. H. Dehmelt, "Less is more: Experiments with an individual atomic particle at rest in free space," Am. J. Phys. 58, 17-27 (1990).
16. C. Sackett et al., "A magnetic suspension system for atoms and bar magnets," Am. J. Phys. 61, 304-309 (1993).