Bibliography: Newton's Clock
 

Newton's Clock: Chaos in the Solar System

With astronomical questions inspiring new mathematics, the remarkable insights of Johannes Kepler, Isaac Newton, and Henri Poincaré paved the way to celestial mechanics— and modern notions of chaotic dynamics. The result is a new picture of a solar system less placid and predictable that its venerable clockwork image would suggest.

Online Bibliography

General

Ekeland, I. 1988. Mathematics and the Unexpected. University of Chicago Press.

Peterson, I. 1993. Newton's Clock: Chaos in the Solar System. W.H. Freeman.

Stewart, I. 1989. Does God Play Dice? The Mathematics of Chaos. Basil Blackwell. 

Motion

Peterson, I. 2000. Tilt-A-Whirl chaos (I). MAA Online (April 24).

______. 2000. Tilt-A-Whirl Chaos (II). MAA Online (May 1).

Shinbrot, T., C. Grebogi, J. Wisdom, and J.A. Yorke. 1992. Chaos in a double pendulum. American Journal of Physics 60(June):491-499.

Ancient Astronomy

Peterson, I. 1997. Fractions, cycles, and time. MAA Online (Oct. 13).

Columbus

Gingerich, O. 1992. Astronomy in the age of Columbus. Scientific American 267(November):100-105.

Olson, D.W. 1992. Columbus and an eclipse of the moon. Sky & Telescope 84(October):437-440. 

Peterson, I.  2006. The eclipse that saved Columbus. MAA Online (Oct. 9).

Steel, D. 2001. Eclipse: The Celestial Phenomenon That Changed the Course of History. Joseph Henry Press.

Kepler and Newton

Arnol'd, V.I. 1990. Huygens and Barrow, Newton and Hooke. Birkhauser.

Arnol'd, V.I. and V.A. Vasil'ev. 1989. Newton's Principia read 300 years later. Notices of the American Mathematical Society 36(November):1148-1154.

Fauvel, J., R. Flood, M. Shortland, and R. Wilson, eds. 1988. Let Newton Be! A New Perspective on His Life and Works. Oxford University Press.

Gingerich, O. 1992. The Great Copernicus Chase and Other Adventures in Astronomical History. Sky Publishing.

Stephenson, B. 1987. Kepler's Physical Astronomy. Springer-Verlag.

Thoren, V.E. 1990. The Lord of Uraniborg: A Biography of Tycho Brahe. Cambridge University Press.

Westfall, R.S. 1987. The achievement of Isaac Newton: An essay on the occasion of the three hundredth anniversary of the Principia. Mathematical Intelligencer 9(No. 4):45-49.

______. 1980. Never at Rest: A Biography of Isaac Newton. Cambridge University Press.

Three-Body Problem

Barrow-Green, J. 1997. Poincaré and the Three Body Problem. American Mathematical Society.

Diacu, F. 1996. The solution of the n-body problem. Mathematical Intelligencer 18(No. 3):66-70.

Diacu, F., and P. Holmes. 1996. Celestial Encounters: The Origins of Chaos and Stability. Princeton University Press.

Gutzwiller, M.C. 1998. Moon-Earth-Sun: The oldest three-body problem. Reviews of Modern Physics 70(April):589-639.

Holmes, P. 1990. Poincaré, celestial mechanics, dynamical-systems theory and "chaos." Physics Reports 193(September):137-163.

Peterson, 1. 1999. Prophet of chaos. MAA Online (Nov. 15).

Poincaré, J.H. 1993. New Methods of Celestial Mechanics, D. Goroff, ed. American Institute of Physics.

______. 1890. Sur le problème des trois corps at les équations de la dynamique. Acta Mathematica 13:1-270.

Solar System Stability

Freedman, D.H. 1990. Gravity's revenge. Discover 11(May):54-60.

Hartley, K. 1990. Solar system chaos. Astronomy 18(May):34-39.

Kerr, R.A. 1992. From Mercury to Pluto, chaos pervades the solar system. Science 257(July 3):33.

______. 1989. Does chaos permeate the solar system? Science 244(April 14):144-145.

Killian, A.M. 1989. Playing dice with the solar system. Sky & Telescope 78(August):136-140.

Malhotra, R.,  M. Holman, and T. Ito. 2001. Chaos and stability of the solar system. Proceedings of the National Academy of Sciences 98(Oct. 23):12342-12343.

Moser, J. 1978. Is the solar system stable? Mathematical Intelligencer 1(No. 2):65-71.

Murray, C. Is the solar system stable? New Scientist 124(Nov. 25):60-63.

Sussman, G.J., and J. Wisdom. 1992. Chaotic evolution of the solar system. Science 257(July 3):56-62.

Wisdom, J. 1987. Urey Prize lecture: Chaotic dynamics in the solar system. Icarus 72(November):241-275.