Bibliography for the Pendulum


  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. Robust Nonlinear H2/H∞ Control for a Parallel Inverted Pendulum with Dry Friction
    Han, S. I.; Kim, J. S.; Choi, J. W.
    JSME International Journal Series C, 2002, vol. 45, no. 1, pp. 194-203, Ingenta.  
  3. Effect of Nonlinear Stiffness on the Motion of a Flexible Pendulum
    Zaki, K.; Noah, S.; Rajagopal, K. R.; Srinivasa, A. R.
    Nonlinear Dynamics, 2002, vol. 27, no. 1, pp. 1-18, Ingenta.  
  4. One nonlinear differential equation and operation of hydraulic dissipative pendulum.
    Dorovsky, V. N.
    Comput. Math. Appl. 41 (2001), no. 5-6, 697--702, Math. Sci. Net.  
  5. Nonlinear swing up control of inverted pendulum via Lyapunov function approach. (Japanese)
    Higashi, Kenichi; Suemitsu, Haruo; Matsuo, Takami
    Rep. Fac. Engrg. Oita Univ. No. 44 (2001), 79--86, Math. Sci. Net.  
  6. 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.  
  7. Nonlinear behaviour in a torsion pendulum
    Milotti, E.
    European Journal of Physics, 2001, vol. 22, no. 3, pp. 239-248, Ingenta.  
  8. Nonlinear Dynamics of a Harmonically-Excited Inelastic Inverted Pendulum
    Williamson, E. B.; Hjelmstad, K. D.
    Journal of Engineering Mechanics, 2001, vol. 127, no. 1, pp. 52-57, Ingenta.  
  9. 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.  
  10. 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.  
  11. Robust Controller for Nonlinear & Unstable System: Inverted Pendulum
    Mirza, A.; Hussain, S.
    Advances in Modelling and Analysis, 2000, vol. 55, no. 3/4, pp. 49 I-60 I, Ingenta.  
  12. Predictive Control of Nonlinear Mechanical Systems Using a Short-Term Prediction Method Based on Chaos Theory: Applications to a Forced Pendulum
    Masumoto, N.; Yamakawa, H.
    Asme, 2000, vol. 61, pp. 165-172, Ingenta.  
  13. Nonlinear Ordinary Boundary Value Problems under a Combined Effect of Periodic and Attractive Nonlinearities
    A. Cañada
    Journal of Mathematical Analysis and Applications, Vol. 243, No. 1, Mar 2000, pp. 174-189, Ideal.  
  14. 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.  
  15. Branches of Forced Oscillations for Periodically Perturbed Second Order Autonomous ODEs on Manifolds
    Massimo Furi, Marco Spadini
    Journal of Differential Equations, Vol. 154, No. 1, May 1999, pp. 96-106, Ideal.  
  16. The Inverted Pendulum: A Singularity Theory Approach
    H. W. Broer, I. Hoveijn, M. van Noort, G. Vegter
    Journal of Differential Equations, Vol. 157, No. 1, Sep 1999, pp. 120-149, Ideal.  
  17. A remark on random perturbations of the nonlinear pendulum  
    Freidlin, Mark; Weber, Matthias  
    Ann. Appl. Probab. 9 (1999), no. 3, 611--628, Math. Sci. Net.  
  18. Control of the oscillation of a pendulum with limited torque---an application of human simulated intelligent control to a nonlinear system. (Chinese)
    Li, Zu Shu
    Control Theory Appl. 16 (1999), no. 2, 225--229, Math. Sci. Net.  
  19. Nonlinear generalize equations of motion for multi-link inverted pendulum systems.
    Eltohamy, Khalad Gamel; Kuo, Chen-Yuan
    International journal of systems science, 1999, vol. 30, no. 5, pp. 505, Ingenta.  
  20. Controlling Chaos Using Nonlinear Approximations for a Pendulum with Feedforward and Feedback Control.
    Yagasaki, K.; Yamashita, S.
    International journal of bifurcation and chaos in applied sciences and engineering, 1999, vol. 9, no. 1, pp. 233, Ingenta.  
  21. Nonlinear optimal control of a triple link inverted pendulum with single control input.
    Eltohamy, Khaled Gamal; Kuo, Chen-Yuan
    Internat. J. Control 69 (1998), no. 2, 239--256, Math. Sci. Net.  
  22. 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.  
  23. Nonlinear optimal control of a triple link inverted pendulum with single control input.
    Eltohamy, K.G.; Kuo, C.-Y.
    International journal of control, 1998, vol. 69, no. 2, pp. 239, Ingenta.  
  24. Gudermann and the Simple Pendulum  
    John S. Robertson  
    College Math Journal: Volume 28, Number 4, (1997), Pages: 292-295.
  25. Dussy, Stéphane; El Ghaoui, Laurent Multi-objective bounded control of uncertain nonlinear systems: an
    inverted pendulum example. Control of uncertain systems with bounded inputs, 55--73, Lecture Notes in Control and
    Inform. Sci., 227, Springer, London, 1997, Math. Sci. Net.  
  26. Mode competition in a system of two parametrically driven pendulums with nonlinear coupling.
    Banning, E. J.; van der Weele, J. P.; Ross, J. C.; Kettenis, M. M.
    Phys. A 245 (1997), no. 1-2, 49--98, Math. Sci. Net.  
  27. On the Stability of Periodic Solutions of the Damped Pendulum Equation
    Jan epika, Pavel Drábek, Jolana Jeníková
    Journal of Mathematical Analysis and Applications, Vol. 209, No. 2, May 1997, pp. 712-723 (doi: 10.1006/jmaa.1997.5380), Ideal.  
  28. Nonlinear dynamics of a sinusoidally driven pendulum in a repulsive magnetic field.
    Siahmakoun, Azad; French, Valentina A.; Patterson, Jeffrey
    American journal of physics, 1997, vol. 65, no. 5, pp. 393, Ingenta.  
  29. Probabilistic analysis of a nonlinear pendulum  
    Roy, R. Valéry
    Acta Mech. 115 (1996), no. 1-4, 87--101, Math. Sci. Net.  
  30. Investigation of nonlinear oscillations of a compound pendulum.
    Zhuravlev, V.F.
    Mechanics of solids, 1996, vol. 31, no. 3, pp. 137, Ingenta.  
  31. 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.  
  32. Geometry and the Foucault Pendulum  
    John Oprea  
    American Mathematical Monthly, Vol. 102, No. 6. (Jun. - Jul., 1995), pp. 515-522, Jstor.  
  33. 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.  
  34. Nonlinear control of a swinging pendulum.
    Chung, Chung Choo; Hauser, John
    Automatica J. IFAC 31 (1995), no. 6, 851--862, Math. Sci. Net.  
  35. Nonlinear controller for an inverted pendulum having restricted travel.
    Wei, Qifeng; Dayawansa, W. P.; Levine, W. S.
    Automatica J. IFAC 31 (1995), no. 6, 841--850, Math. Sci. Net.  
  36. Teaching the Nonlinear Pendulum  
    Zheng, T.F.; Mears, M.; Hall, D.
    The Physics teacher, 1994, vol. 32, no. 4, pp. 248, Ingenta.  
  37. Approaching nonlinear dynamics by studying the motion of a pendulum. III. Predictability and control of chaotic motion.
    Hübinger, B.; Doerner, R.; Heng, H.; Martienssen, W.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 4 (1994), no. 4, 773--784, Math. Sci. Net.  
  38. Approaching nonlinear dynamics by studying the motion of a pendulum. II. Analyzing chaotic motion.
    Doerner, R.; Hübinger, B.; Heng, H.; Martienssen, W.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 4 (1994), no. 4, 761--771, Math. Sci. Net.  
  39. Approaching nonlinear dynamics by studying the motion of a pendulum. I. Observing trajectories in state space.
    Heng, H.; Doerner, R.; Hübinger, B.; Martienssen, W.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 4 (1994), no. 4, 751--760, Math. Sci. Net.  
  40. Renormalizing the Simple Pendulum (in Classroom Notes)  
    Shaun Bullett, Jaroslav Stark  
    SIAM Review, Vol. 35, No. 4. (Dec., 1993), pp. 631-640, Jstor.  
  41. 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.  
  42. Bifurcation of positive solutions of generalized nonlinear undamped pendulum problems.
    Wang, Shin Hwa
    Bull. Inst. Math. Acad. Sinica 21 (1993), no. 3, 211--227, Math. Sci. Net.  
  43. 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.  
  44. 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.  
  45. Les oscillations forcées du pendule: un paradigme en dynamique et en analyse non linéaire. (French)
    Mawhin, Jean
    [Forced oscillations of the pendulum: a paradigm in dynamics and in nonlinear analysis]
    Acad. Roy. Belg. Bull. Cl. Sci. (5) 75 (1989), no. 2-3, 58--68, Math. Sci. Net.  
  46. 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.  
  47. 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.  
  48. The forced pendulum: a paradigm for nonlinear analysis and dynamical systems.
    Mawhin, Jean
    Exposition. Math. 6 (1988), no. 3, 271--287, Math. Sci. Net.  
  49. 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.  
  50. Pendulum in a Variable Medium: Problem 85-5 (in Problems)  
    M. A. Abdelkader  
    SIAM Review, Vol. 27, No. 1. (Mar., 1985), p. 80, Jstor.  
  51. Experiments on the bifurcation behaviour of a forced nonlinear pendulum
    Beckert, S.; Schock, U.; Schulz, C.-D.; Weidlich, T.; Kaiser, F.
    Phys. Lett. A 107 (1985), no. 8, 347--350, Math. Sci. Net.  
  52. Problem 83-14: Pendulum with Variable Length (in Problems)  
    M. A. Abdekader  
    SIAM Review, Vol. 25, No. 3. (Jul., 1983), pp. 402-403, Jstor.  
  53. The elastic pendulum: a nonlinear paradigm.
    Breitenberger, Ernst; Mueller, Robert D.
    J. Math. Phys. 22 (1981), no. 6, 1196--1210, Math. Sci. Net.  
  54. 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.  
  55. The essentially nonlinear case of the motion of a pendulum system. (Russian)
    Besetja, A. P.
    Èlektroènerget. i Avtomat. (Kishinev) Vyp. 22 (1975), 74--81, 116, Math. Sci. Net.  
  56. The Nonlinear Simple Pendulum  
    Fred Brauer  
    American Mathematical Monthly, Vol. 79, No. 4. (Apr., 1972), pp. 348-355, Jstor.  
  57. Galileo on the Isochrony of the Pendulum  
    Piero Ariotti  
    Isis, Vol. 59, No. 4. (Winter, 1968), pp. 414-426, Jstor.  
  58. 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.  
  59. 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.  
  60. 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.  
  61. 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.  
  62. The Spherical Pendulum and Complex Integration  
    Alexander Weinstein  
    American Mathematical Monthly, Vol. 49, No. 8. (Oct., 1942), pp. 521-523, Jstor.  
  63. The Generalized Double Pendulum  
    G. Baley Price  
    American Journal of Mathematics, Vol. 57, No. 4. (Oct., 1935), pp. 928-936, Math. Sci. Net.  
  64. Lagrange's Compound Pendulum  
    H. Bateman  
    American Mathematical Monthly, Vol. 38, No. 1. (Jan., 1931), pp. 1-8, Jstor.  
  65. Foucault's Pendulum in Elliptic Space  
    James Pierpont  
    Transactions of the American Mathematical Society, Vol. 31, No. 3. (Jul., 1929), pp. 444-447, Jstor.  
  66. A Note on Foucault's Pendulum  
    James Pierpont  
    American Mathematical Monthly, Vol. 36, No. 3. (Mar., 1929), pp. 161-162, Jstor.  
  67. On Foucault's Pendulum  
    William Duncan MacMillan  
    American Journal of Mathematics, Vol. 37, No. 1. (Jan., 1915), pp. 95-106, Jstor.  
  68. 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.  
  69. On Foucault's Pendulum  
    A. S. Chessin  
    American Journal of Mathematics, Vol. 17, No. 1. (Jan., 1895), pp. 81-88, Jstor.  
  70. 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