Erratum: Coexisting chaotic and periodic dynamics in clock escapements (Philosophical Transactions: Mathematical, Physical and Engineering Sciences (Series A) 28 July 2006) 364, (2539-2563) doi:10.1098/rsta.2006.1839));Coexisting chaotic and periodic dynamics in clock escapements

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

Volumn 364, Issue 1846, 2006, Pages 2539-2564

  Moon, Francis C ^a   Stiefel, Preston D ^b  

^a Cornell University   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Chaos; Clock; Noise; Nonlinear dynamics

Indexed keywords

EID: 33748295589     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2006.1839     Document Type: Erratum

References (28)

1. Airy, G. B. 1826 On the disturbances of pendulums and balances and the theory of escapements. Trans. Camb. Phil. Soc. III, 105-128. Part I (1830), Plate 2.
2. Andronov, A. A., Vitt, A. A. & Khaikin, S. E. 1966 Theory of oscillators. Oxford, UK, New York, NY: Pergamon Press, Dover Publication.
3. Baillie, G. H., Clutton, C. & Ilbert, C. A. 1956 Britten's old clocks and watches and their makers, 7th edn. New York, NY: Bonanza Books.
4. Berge, P., Pomeau, Y. & Vidal, C. 1984 Order within chaos. Paris, France: Herman.
5. Brnstein, D. 2000 Escapements, governors, ailerons, gyros, and amplifiers: feedback control and the history of technology. Michigan State University Report.
6. Bloxam, J. M. 1854 On the mathematical theory and practical defects of clock escapements, with a description of a new escapement; and some observations for astronomical and scientific purposes. Memoirs R. Astron. Soc. XXII, 103-150.
7. Boedo, S. 1999 Chaos in offset hydrodynamic rotor bearings. In New applications of nonlinear and chaotic dynamics in mechanics (ed. F. C. Moon), pp. 253-260. Dordrecht, The Netherlands: Kluwer Academic Publisher.
8. Bruton, E. 1968 The longcase clock. New York, NY: F.A. Praeger.
9. Bruton, E. 1979 The history of clocks and watches. London, UK: Orbis Publication.
10. Buckingham, E. 1949 Analytical mechanics of gears. New York, NY: McGraw-Hill.
11. Christini, D. J. & Collins, J. J. 1995 Controlling nonchaotic neuronal noise using chaos control techniques. Phys. Rev. Lett. 75, 2782-2785. (doi:10.1103/PhysRevLett.75.2782)
12. Conway, H. G. 1953-55 Origins of mechanical servo mechanisms. Newcomen Soc. XXIX. 1953-1954, 1954-1955
13. Denison, E.B. 1868 (a.k.a. Lord Grimthorpe) A rudimentary treatise on clocks and watches and bells, 5th edn. London, UK: Virtue and Co.
14. Headrick, M.V. 2001 Clocks and time: clock and watch escapements. See http://ubr.com/clocks/educ/escapem.html.
15. Huygens, C. 1658 Horologium.
16. Johnson, M. A. & Moon, F. C. 2001 Nonlinear techniques to characterize pre-chatter and chatter vibrations in the machining of metals. Int. J. Bifurcat. Chaos 11, 449-467.
17. Kauderer, H. 1958 Nichtlineare mechanik. Second part, Section 4, pp. 415-423. Berlin, Germany: Verlag.
18. Kesteven, M. 1978 On the mathematical theory of clocks. Am. J. Phys. 46, 125-129. (doi:10.1119/1.11369)
19. Lepschy, A. M., Mian, G. A. & Viaro, U. 1992 Feedback control in ancient water and mechanical clocks. IEEE Trans. Educ. 35, 3-10. (doi:10.1109/13.123411)
20. Martinek & Rehor, 1996 Mechanische uhren. Berlin, Germany: Verlag Technik.
21. Moon, F. C. 1992 Chaotic and fractal dynamics. New York, NY: Wiley.
22. Moon, F. C. 2003 Franz Reuleaux; contributions to 19th century kinematics and theory of machines. Appl. Mech. Rev. 56, 261-285. (doi:10.1115/1.1523427)
23. Moon, F. C. 2005 Chaotic clocks: a paradigm for the evolution of noise in machines. In IUTAM Symposium Chaotic Dynamics and Control of Systems and Processes in Mechanics, Proceedings (ed. G. Rega), pp. 3-16. Dordecht, The Netherlands, New York, NY: Kluwer, Springer.
24. Moon, F. C., Johnson, M. A. & Holmes, W. T. 1996 Controlling chaos in a two well oscillator. Int. J. Bifurcat. Chaos 6, 337-347. (doi:10.1142/S0218127496000084)
25. Moon, F. C., Reddy, A. J. & Holmes, W. T. 2003 Experiments in control and anti-control of chaos in a dry friction oscillator. J. Vibrat. Control 9, 387-397.
26. Pao, Y.-H., Keh, D.-C. & Howard, S. 1998 Dynamic response and wave propagation in plane trusses and frames. AIAA J. 37, 594-603.
27. Reuleaux, F. 1893 The constructor. (Transl. H. Suplee). Philadelpha, PA: H.H. Suplee.
28. Roup, A. V., Bernstein, D. S., Nersesov, S. G., Haddad, W. M. & Chellaboina, V. 2001 Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and poincare maps. Michigan State University Report.