Bibliography for the Pendulum

short

  1. Interactions between impurities and nonlinear waves in a driven nonlinear pendulum chain
    Chen, W.; Hu, B.; Zhang, H.
    Physical Review, 2002, vol. 65, no. 13, pp. 134302, Ingenta.  
  2. Distinguishing Periodic and Chaotic Time Series Obtained from an Experimental Nonlinear Pendulum
    Franca, L. F. P.; Savi, M. A.
    Nonlinear Dynamics, 2001, vol. 26, no. 3, pp. 253-271, Ingenta.  
  3. An analysis of a nonlinear pendulum-type equation arising in smectic C liquid crystals  
    Barclay, G. J.; Stewart, I. W.
    J. Phys. A 33 (2000), no. 25, 4599--4609, Math. Sci. Net.  
  4. On the Range of Certain Pendulum-Type Equations
    Petr Girg, Francisco Roca  
    Journal of Mathematical Analysis and Applications, Vol. 249, No. 2, (2000), pp. 445-462, Math. Sci. Net.  
  5. Experimental study of Chaos in a driven triple pendulum  
    Q. Zhu, M. Ishitobi  
    Journal of Sound and Vibration, Vol. 227, No. 1, Oct 1999, pp. 230-238, Ideal.  
  6. Sensitive dependence on initial conditions of strongly nonlinear periodic orbits of the forced pendulum.
    Pilipchuk, V. N.; Vakakis, A. F.; Azeez, M. A. F.
    Nonlinear Dynam. 16 (1998), no. 3, 223--237, Math. Sci. Net.  
  7. Gudermann and the Simple Pendulum  
    John S. Robertson  
    College Math Journal: Volume 28, Number 4, (1997), Pages: 292-295.
  8. Probabilistic analysis of a nonlinear pendulum  
    Roy, R. Valéry
    Acta Mech. 115 (1996), no. 1-4, 87--101, Math. Sci. Net.  
  9. The Geometrical Description of the Nonlinear Dynamics of a Multiple Pendulum  
    V. Zharnitsky  
    SIAM Journal on Applied Mathematics, Vol. 55, No. 6. (Dec., 1995), pp. 1753-1763, Jstor.  
  10. Geometry and the Foucault Pendulum  
    John Oprea  
    American Mathematical Monthly, Vol. 102, No. 6. (Jun. - Jul., 1995), pp. 515-522, Jstor.  
  11. Stabilization of the Inverted Linearized Pendulum by High Frequency Vibrations  
    Mark Levi, Warren Weckesser  
    SIAM Review, Vol. 37, No. 2. (Jun., 1995), pp. 219-223, Jstor.  
  12. Nonlinear control of a swinging pendulum.
    Chung, Chung Choo; Hauser, John
    Automatica J. IFAC 31 (1995), no. 6, 851--862, Math. Sci. Net.  
  13. Teaching the Nonlinear Pendulum  
    Zheng, T.F.; Mears, M.; Hall, D.
    The Physics teacher, 1994, vol. 32, no. 4, pp. 248, Ingenta.  
  14. Renormalizing the Simple Pendulum (in Classroom Notes)  
    Shaun Bullett, Jaroslav Stark  
    SIAM Review, Vol. 35, No. 4. (Dec., 1993), pp. 631-640, Jstor.  
  15. Chaotic Motion of a Pendulum with Oscillatory Forcing  
    S. P. Hastings, J. B. McLeod  
    American Mathematical Monthly, Vol. 100, No. 6. (Jun. - Jul., 1993), pp. 563-572, Jstor.  
  16. Deterministic chaos in the elastic pendulum: a simple laboratory for nonlinear dynamics.
    Cuerno, R.; Rañada, A. F.; Ruiz-Lorenzo, J. J.
    Amer. J. Phys. 60 (1992), no. 1, 73--79, Math. Sci. Net.  
  17. Remarks on Forced Equations of the Double Pendulum Type  
    Gabriella Tarantello  
    Transactions of the American Mathematical Society, Vol. 326, No. 1. (Jul., 1991), pp. 441-452, Jstor.  
  18. Lyapunov Optimal Feedback Control of a Nonlinear Inverted Pendulum.
    Anderson, M.J.; Grantham, W.J.
    Transactions of the asme. journal of dynamic sy, 1989, vol. 111, no. 4, pp. 554, Ingenta.  
  19. Stability of the Inverted Pendulum--A Topological Explanation (in Classroom Notes)  
    Mark Levi  
    SIAM Review, Vol. 30, No. 4. (Dec., 1988), pp. 639-644, Jstor.  
  20. The forced pendulum: a paradigm for nonlinear analysis and dynamical systems.
    Mawhin, Jean
    Exposition. Math. 6 (1988), no. 3, 271--287, Math. Sci. Net.  
  21. Power Series Solution to a Simple Pendulum with Oscillating Support  
    Mohammad B. Dadfar, James F. Geer  
    SIAM Journal on Applied Mathematics, Vol. 47, No. 4. (Aug., 1987), pp. 737-750, Jstor.  
  22. Pendulum in a Variable Medium: Problem 85-5 (in Problems)  
    M. A. Abdelkader  
    SIAM Review, Vol. 27, No. 1. (Mar., 1985), p. 80, Jstor.  
  23. Problem 83-14: Pendulum with Variable Length (in Problems)  
    M. A. Abdekader  
    SIAM Review, Vol. 25, No. 3. (Jul., 1983), pp. 402-403, Jstor.  
  24. The elastic pendulum: a nonlinear paradigm.
    Breitenberger, Ernst; Mueller, Robert D.
    J. Math. Phys. 22 (1981), no. 6, 1196--1210, Math. Sci. Net.  
  25. Galileo's Need for Precision: The "Point" of the Fourth Day Pendulum Experiment (in Notes & Correspondence)  
    Ronald Naylor
    Isis, Vol. 68, No. 1. (Mar., 1977), pp. 97-103, Jstor.  
  26. The Nonlinear Simple Pendulum  
    Fred Brauer  
    American Mathematical Monthly, Vol. 79, No. 4. (Apr., 1972), pp. 348-355, Jstor.  
  27. Galileo on the Isochrony of the Pendulum  
    Piero Ariotti  
    Isis, Vol. 59, No. 4. (Winter, 1968), pp. 414-426, Jstor.  
  28. Effect of Vibration on the Accuracy of a Vertical Reference Pendulum  
    T. K. Caughey  
    SIAM Journal on Applied Mathematics, Vol. 15, No. 5. (Sep., 1967), pp. 1199-1208, Jstor.  
  29. The Asymptotic Behavior of Solutions of Pendulum-Type Equations  
    George Seifert  
    The Annals of Mathematics, 2nd Ser., Vol. 69, No. 1. (Jan., 1959), pp. 75-87, Jstor.  
  30. Limiting Sets of Trajectories of a Pendulum-Type System  
    George Seifert  
    Proceedings of the American Mathematical Society, Vol. 7, No. 6. (Dec., 1956), pp. 1082-1084, Jstor.  
  31. Contour Integration in the Theory of the Spherical Pendulum and the Heavy Symmetrical Top  
    Walter Kohn  
    Transactions of the American Mathematical Society, Vol. 59, No. 1. (Jan., 1946), pp. 107-131, Jstor.  
  32. The Spherical Pendulum and Complex Integration  
    Alexander Weinstein  
    American Mathematical Monthly, Vol. 49, No. 8. (Oct., 1942), pp. 521-523, Jstor.  
  33. The Generalized Double Pendulum  
    G. Baley Price  
    American Journal of Mathematics, Vol. 57, No. 4. (Oct., 1935), pp. 928-936, Math. Sci. Net.  
  34. Lagrange's Compound Pendulum  
    H. Bateman  
    American Mathematical Monthly, Vol. 38, No. 1. (Jan., 1931), pp. 1-8, Jstor.  
  35. Foucault's Pendulum in Elliptic Space  
    James Pierpont  
    Transactions of the American Mathematical Society, Vol. 31, No. 3. (Jul., 1929), pp. 444-447, Jstor.  
  36. A Note on Foucault's Pendulum  
    James Pierpont  
    American Mathematical Monthly, Vol. 36, No. 3. (Mar., 1929), pp. 161-162, Jstor.  
  37. On Foucault's Pendulum  
    William Duncan MacMillan  
    American Journal of Mathematics, Vol. 37, No. 1. (Jan., 1915), pp. 95-106, Jstor.  
  38. The Deflecting Force of the Earth's Rotation and Foucault's Pendulum: An Elementary Analysis  
    W. H. Jackson  
    American Mathematical Monthly, Vol. 16, No. 5. (May, 1909), pp. 82-85, Jstor.  
  39. On Foucault's Pendulum  
    A. S. Chessin  
    American Journal of Mathematics, Vol. 17, No. 1. (Jan., 1895), pp. 81-88, Jstor.  
  40. A Pendulum Whose Time of Oscillation Is Independent of the Position of Its Centre of Gravity  
    R. J. Adcock  
    The Analyst, Vol. 9, No. 4. (Jul., 1882), p. 119, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003