Chandler Wobble: Stochastic and Deterministic Dynamics

  • Alejandro JenkinsEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 182)


We propose a model of the Earth’s torqueless precession, the “Chandler wobble,” as a self-oscillation driven by positive feedback between the wobble and the centrifugal deformation of the portion of the Earth’s mass contained in circulating fluids. The wobble may thus run like a heat engine, extracting energy from heat-powered geophysical circulations whose natural periods would otherwise by unrelated to the wobble’s observed period of about fourteen months. This can explain, more plausibly than previous models based on stochastic perturbations or forced resonance, how the wobble is maintained against viscous dissipation. The self-oscillation is a deterministic process, but stochastic variations in the magnitude and distribution of the circulations may turn off the positive feedback (a Hopf bifurcation), accounting for the occasional extinctions, followed by random phase jumps, seen in the data. This model may have implications for broader questions about the relation between stochastic and deterministic dynamics in complex systems, and the statistical analysis thereof.


Hopf Bifurcation Polar Motion Heat Engine Stochastic Perturbation Chandler Wobble 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author thanks Eric Alfaro, Jorge Amador, and Paul O’Gorman for discussions on meteorological issues, as well as Howard Georgi and José Gracia-Bondía for encouragement and advice on this project.


  1. 1.
    L. Euler, Theoria motus corporum solidorum seu rigidorum (A. F. Rose, Rostock & Greifswald, 1765)Google Scholar
  2. 2.
    L. D. Landau, E. M. Lifshitz, Mechanics, 3rd edn. (Elsevier, Oxford, 1976)zbMATHGoogle Scholar
  3. 3.
    F. Klein, A. Sommerfeld, The Theory of the Top, vol. III (Birkhäuser, New York, 2012 [1903])Google Scholar
  4. 4.
    S. C. Chandler, “On the variation of latitude, I”, Astron. J. 11 (1891), 59–61CrossRefGoogle Scholar
  5. 5.
    S. C. Chandler, “On the variation of latitude, II”, Astron. J. 11 (1891), 65–70CrossRefGoogle Scholar
  6. 6.
    W. E. Carter, M. S. Carter, “Seth Carlo Chandler, Jr. 1846–1913”, in Biographical Memoirs 66 (National Academy of Sciences, Washington, D.C., 1995), 44–79Google Scholar
  7. 7.
    C. R. Wilson, R. O. Vicente, “Maximum likelihood estimates of polar motion parameters”, in Variations in Earth Rotation, eds. D. D. McCarthy and W. E. Carter (American Geophysical Union, Geophysical Monograph Series 59, 1990), 151–155Google Scholar
  8. 8.
    S. Newcomb, “On the dynamics of the Earth’s rotation, with respect to the periodic variations of latitude”, Mon. Not. R. Astron. Soc. 52 (1892), 336–341CrossRefzbMATHGoogle Scholar
  9. 9.
    H. Jeffreys, “The variation of latitude”, Mon. Not. R. Astron. Soc. 100 (1940), 139–155CrossRefGoogle Scholar
  10. 10.
    H. Jeffreys, “The variation of latitude”, Mon. Not. R. Astron. Soc. 141 (1968), 255–268CrossRefGoogle Scholar
  11. 11.
    H.-P. Plag, “Chandler wobble and pole tide in relation to interannual atmosphere-ocean dynamics”, in Tidal Phenomena (Springer, Lecture Notes on Earth Sciences 66, 1997), 183–218CrossRefGoogle Scholar
  12. 12.
    R. S. Gross, “The excitation of the Chandler wobble”, Geophys. Res. Lett. 27 (2000), 2329–2332CrossRefGoogle Scholar
  13. 13.
    Y. Aoyama, I. Naito, “Atmospheric excitation of the Chandler wobble, 1983–1998”, J. Geophys. Res. 106 (2001), 8941–8954CrossRefGoogle Scholar
  14. 14.
    Y. Aoyama et al., “Atmospheric quasi-14 month fluctuation and excitation of the Chandler wobble”, Earth Planets Space 55 (2003), e25–e28CrossRefGoogle Scholar
  15. 15.
    A. A. Andronov, A. A. Vitt, S. È. Khaĭkin, Theory of Oscillators (Dover, Mineola, 1987 [1966])Google Scholar
  16. 16.
    A. Jenkins, “Self-oscillation”, Phys. Rep. 525 (2013), 167–222MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    S. H. Strogatz et al., “Theoretical mechanics: Crowd synchrony on the Millennium Bridge”, Nature 403 (2005) 43–44CrossRefGoogle Scholar
  18. 18.
    G. B. Airy, “On certain Conditions under which a Perpetual Motion is possible”, Trans. Cambridge Phil. Soc. 3 (1830), 369–372Google Scholar
  19. 19.
    R. Willis, “On the Mechanism of the Larynx”, Trans. Cambridge Phil. Soc. 4 (1833), 323–352. This work was originally presented in May 1829.Google Scholar
  20. 20.
    Z. Malkin, N. Miller, “Chandler wobble: two more large phase jumps revealed”, Earth Planets Space 62 (2010), 943–947CrossRefGoogle Scholar
  21. 21.
    K. Lambeck, The Earth’s Variable Rotation (Cambridge U. P., Cambridge 1980)CrossRefGoogle Scholar
  22. 22.
    F. D. Stacey, P. M. Davis, Physics of the Earth, 4th edn. (Cambridge U. P., Cambridge, 2008)CrossRefzbMATHGoogle Scholar
  23. 23.
    A. Souriau, “The influence of earthquakes on the polar motion”, in Earth Rotation: Solved and Unsolved Problems, ed. A. Cazenave (Reidel, Dordrecht, 1986), 229–249CrossRefGoogle Scholar
  24. 24.
    B. F. Chao, R. S. Gross, “Changes in the Earth’s rotation and low-degree gravitational field induced by earthquakes”, Geophys. J. Roy. Astr. S. 91 (1987), 569–596CrossRefGoogle Scholar
  25. 25.
    V. Frède, P. Mazzega, “Detectability of deterministic non-linear processes in Earth rotation time-series I. Embedding”, Geophys. J. Int. 137 (1999), 551–564CrossRefGoogle Scholar
  26. 26.
    V. Frède, P. Mazzega, “Detectability of deterministic non-linear processes in Earth rotation time-series II. Dynamics”, Geophys. J. Int. 137 (1999), 565–579CrossRefGoogle Scholar
  27. 27.
    V. Frède, P. Mazzega. “A preliminary nonlinear analysis of the Earth’s Chandler wobble”, Discrete Dyn. Nat. Soc. 4 (2000), 39–53CrossRefGoogle Scholar
  28. 28.
    B. B. Mandelbrot, K. McCamy, “On the Secular Pole Motion and the Chandler Wobble”, Geophys. J. R. astro. Soc. 21 (1970), 217–232Google Scholar
  29. 29.
    D. J. Tritton, Physical Fluid Dynamics, 2nd edn. (Oxford U. P., Oxford, 1998)zbMATHGoogle Scholar
  30. 30.
    H. Georgi, The Physics of Waves (Prentice Hall, Englewood Cliffs, 1993)Google Scholar
  31. 31.
    D. Volchenkov, T. Krüger, P. Blanchard, “Heavy-tailed Distributions In Some Stochastic Dynamical Models", Discontinuity Nonlinearity Complexity 1 (2012), 1–40Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Escuela de FísicaUniversidad de Costa RicaSan JoséCosta Rica
  2. 2.Academia Nacional de CienciasSan JoséCosta Rica

Personalised recommendations