Synchronization of two coupled escapement-driven pendulum clocks

Journal of Sound and Vibration

Volumn 291, Issue 3-5, 2006, Pages 566-603

  Senator, M ^a  

^a Stevens Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; MECHANICAL CLOCKS; NONLINEAR SYSTEMS; SYNCHRONIZATION;

HUYGEN'S SYSTEMS; PENDULUM CLOCKS;

PENDULUMS;

EID: 31644433452     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2005.06.018     Document Type: Article

References (19)

1. R. Mirollo, and S. Strogatz Synchronization of pulse-coupled biological oscillators SIAM Journal of Applied Mathematics 50 6 1990 1645 1662
2. C. Huygens, Letter to de Sluse in Oeuveres Complètes de Christiaan Huygens [referred to as O.C. in the references that follow] 5, Correspondance 1664-1665, published for the Société Hollandaise Des Sciences by Martinus Nijhoff, La Haye (1893), Letter No. 1333 of 24 February 1665, 241.
3. C. Huygens, Attachment to a letter to Constantyn Huygens, his father, in: O.C. 5, Letter No. 1335 of 26 February 1665, pp. 243-244.
4. C. Huygens, O.C. 17, L'Horloge a pendule de 1651 a 1666, Martinus Nijhoff, La Haye, 1932, pp. 183-187.
5. C. Huygens, Letter to Moray in O.C. 5, Letter No. 1345 of 6 March 1665, pp. 255-256.
6. C. Huygens, O.C. 18, Horologium Oscillatorium (1673), Martinus Nijhoff, La Haye, 1934, pp. 69-368.
7. C. Huygens, Christiaan Huygens' The Pendulum Clock or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks, Translated by R.J. Blackwell, The Iowa State University Press, Ames, Iowa, 1988.
8. D.J. Korteweg, Les Horloges sympathiques de Huygens, les phénomènes connexes et les oscillations principales et composées que présentent deux pendules fixés à un mécanisme à un seul degré de liberté, in: Archives Néerlandaises d. Sciences ex. et nat. Serie II, T. XI, M. Nijhoff, La Haye, 1906, 273-295.
9. I.I. Blekhman Synchronization in Science and Technology 1988 ASME Press New York (This book is an English translation of Sinkhronizatsiia v prirode i tekhnike, Nauka Publishers, Moscow, 1981)
10. M. Bennett, M.F. Schatz, H. Rockwood, and K. Wiesenfeld Huygens' clocks Proceedings Royal Society A 458 2019 2002 563 580
11. J. Pantaleone Synchronization of metronomes American Journal of Physics 70 10 2002 992 1000
12. A.A. Andronov, A.A. Vitt, S.E. Khaikin, Theory of Oscillators, Translated by F. Immirzi, Edited and Abridged by W. Fishwick, Pergamon Press, Oxford, 1966.
13. E.L. Edwardes The Story of the Pendulum Clock 1977 John Sherratt and Son Ltd. Altrincham, UK
14. A.M. Lepschy, G.A. Mian, and U. Viaro Feedback control in ancient water and mechanical clocks IEEE Transactions on Education 35 1 1992 3 10
15. A.V. Roup, D.S. Bernstein, S.G. Nersesov, W.M. Haddad, and V. Chellaboina Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincare maps International Journal of Control 76 17 2003 1685 1698
16. R.E. Mickens An Introduction to Nonlinear Oscillations 1981 Cambridge University Press Cambridge, UK
17. S.H. Strogatz Nonlinear Dynamics and Chaos 1994 Addison-Wesley Reading, MA
18. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery Numerical Recipes in FORTRAN - The Art of Scientific Computing second ed. 1992 Cambridge University Press Cambridge, UK
19. T.S. Parker, and L.O. Chua Practical Numerical Algorithms for Chaotic Systems 1989 Springer New York