Robert Hooke's conical pendulum from the modern viewpoint of amplitude equations and its optical analogues

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2066, 2006, Pages 531-540

  Rousseaux, Germain ^a   Coullet, Pierre ^a   Gilli, Jean Marc ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Amplitude equations; Conical pendulum; Faraday effect; Foucault effect; Nonlinear precession; Self rotation

Indexed keywords

EID: 33845542136     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1587     Document Type: Article

References (21)

1. Acloque, P. 1981 Oscillations et Stabilité selon Foucault, Critique historique et expérimentale, Éditions du CNRS.
2. Airy, G. B. 1851a On the vibration of a free pendulum in an oval differing little from a straight line. R. Astron. Soc. XX, 121-130. (http://home.t01.itscom.net/allais/whiteprior/airy/airyprecession.pdf)
3. Airy, G. B. 1851b On the vibration of a free pendulum in an oval differing little from a straight line. Philos. Mag. Ser. 4 2, 147-149.
4. Bravais, M. A. 1854 Sur l'influence qu'exerce la rotation de la Terre sur le mouvement d'un pendule à oscillations coniques. J. Math. Pures Appl. XIX, 1-50. (http://gallica.bnf.fr/)
5. Brookes Spencer, J. 1970 On the varieties of nineteenth-century magneto-optical discovery. Isis 61, 34-51. (doi:10.1086/350577)
6. Chazy, J. 1930 Sur l'effet pendule sphérique dans l'expérience du pendule de Foucault. Dull. Soc. Math. France 58, 100-104. (http://www.numdam.org/)
7. Diehl Patterson, L. 1952 Pendulums of Wren and Hooke. Osiris 10, 277-321. (doi:10.1086/368556)
8. Gray, C. G., Karl, G. & Novikov, V. A. 2004 Progress in classical and quantum variational principles. Rep. Prog. Phys. 67, 159-208. (doi:10.1088/0034-4885/67/2/R02)
9. Jonsson, F. 2000 The nonlinear optics of magneto-optic media, Department of Physics, Trita-FYS, 2208. Stockholm: KTH. (http://media.lib.kth.se/; http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-2967)
10. Kamerlingh Onnes, H. 1879 Nieuwe Bewijzen voor de Aswenteling der Aarde, PhD thesis, Groningen, J. B. Wolters. (http://www.allais.info/priorartdocs/ kamonnthes.htm)
11. Maker, P. D. & Terhune, R. W. 1964 Study of optical effects due to an induced polarization third order in the electric field strength. Phys. Rev. 137, 801-818. (doi:10.1103/PhysRev.137.A801)
12. Nauenberg, M. 1994 Hooke, orbital dynamics and Newton's principia. Am. J. Phys. 62, 331-350. (doi:10.1119/1.17576)
13. Nauenberg, M. 2005 Robert Hooke's seminal contribution to orbital dynamics. Phys. Perspect. 7(1), pp. 4-34.
14. Olsson, M. G. 1978 The precessing spherical pendulum. Am. J. Phys. 40, 1118. (doi:10.1119/1.11151)
15. Olsson, M. G. 1981 Spherical pendulum revisited. Am. J. Phys. 49, 531. (doi:10.1119/1.12666)
16. Olsson, M. G. & Nelson, W. 1986 The pendulum-rich physics from a simple system. Am. J. Phys. 54, 112. (doi:10.1119/1.14490)
17. Routh, E. J. 1898 A treatise on dynamics of a particle. With numerous examples. Cambridge, UK: Cambridge University Press. (http://name.umdl.umich. edu/ABR4374)
18. Van Baak, D. A. 1996 Resonant Faraday rotation as a probe of atomic dispersion. Am. J. Phys. 64, 724. (doi:10.1119/1.18356)
19. Warwick, A. 1993 Frequency, theorem and formula: remembering Joseph Larmor in electromagnetic theory. Notes Rec. R. Soc. 47, 49-60.
20. Wells, D. A. 1967 Lagrangian dynamics, Schaum's outlines. New York: McGraw Hill.
21. Ya Zeldovich, B. & Soileau, M. J. 2004 Bi-frequency pendulum on a rotary platform: modeling various optical phenomena. Phys. Uspekhi 47, 1239-1255. (doi:10.1070/PU2004v047n12A BEH001880)