Floquet's theorem and matrices for parametric oscillators: Theory and demonstrations

American Journal of Physics

Volumn 67, Issue 2, 1999, Pages 127-132

  Fameli, N ^a   Curzon, F L ^b   Mikoshiba, S ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033444557     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19207     Document Type: Article

References (26)

1. E. D. Courant and H. S. Snyder, "Theory of the alternating gradient synchrotron," Ann. Phys. 3, 1-48 (1958).
2. D. J. Ness, "Small oscillations of a stabilized inverted pendulum," Am. J. Phys. 35, 964-967 (1967).
3. H. P. Kalmus, "The inverted pendulum," Am. J. Phys. 38, 874-878 (1970).
4. M. M. Michaelis, "Stroboscopic studies of the inverted pendulum," Am. J. Phys. 53, 1079-1083 (1985).
5. H. J. T. Smith and J. A. Blackburn, "Experimental study of an inverted pendulum," Am. J. Phys. 60, 903-908 (1992).
6. N. W. McLachlan, Theory and Application of Mathieu Functions (Oxford U.P., London, 1947).
7. L. A. Pipes and L. R. Harvill, Applied Mathematics for Engineers and Physicists (Mc Graw-Hill, New York, 1970), 32nd ed., p. 688.
8. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, London, 1960), p. 80.
9. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, pp. 556-577.
10. See Ref. 7, pp. 683-719.
11. E. D. Yorke, "Square-wave model for a pendulum with oscillating suspension," Am. J. Phys. 46, 285-288 (1978).
12. See Ref. 8, p. 80.
13. See Ref. 7, pp. 683-719.
14. See Ref. 11, pp. 285-288.
15. E. Meissner, Schweiz. Bauz. 72, 95 (1918), cited by in Ref. 7 on p. 684 but not read by us.
16. See Ref. 7, pp. 683-694.
17. See Ref. 11, pp. 285-288.
18. See Ref. 2.
19. See Ref. 3.
20. See Ref. 4.
21. See Ref. 5.
22. P. Horowitz and W. Hill, The Art of Electronics (Cambridge U.P., Cambridge, 1989), 2nd ed., pp. 903-904.
23. S. Raimes, The Wave Mechanics of Electrons in Metals (North-Holland, Amsterdam, 1963), pp. 196-198.
24. F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, Plasma Physics Vol. 1 (Plenum, New York, 1984), 2nd ed., pp. 309-324.
25. C. Pearson, Handbook of Applied Mathematics (Van Nostrand, New York, 1974), p. 730.
26. See Ref. 9, pp. 556-557.