VISUALIZING CHAOS IN DYNAMICS OF DOUBLE PENDULUM

M. O. Olayiwola (Nigeria), A. W. Gbolagade (Nigeria), F. A. Hammed (Nigeria) and I. A. Idowu (Nigeria)

Received November 21, 2007

References:

[1] A. Boucke and H Baxa, Theoretische Mechanik, VEB Deutscher Verlag der Wissenschaften, 1973, pp. 234-237. [2] R. Carretero et al., Regular and chaotic behavior in an extensible pendulum, European J. Phys. (2003), 139-148. [3] P. Contopoulos, Dynamical Systems and Chaos, Proceedings of the International Congress of Mathematicians, Stockholm V (1963), 500-508. [4] T. Csendes and Banhelyi, Towards a computer-assisted proof for chaos in a forced damped pendulum equation, Elsevier, 2005 (Preprint). [5] B. García-Archilla, J. M. Sanz-Serna and R. D. Skeel, Long-time-step methods for oscillatory differential equations, SIAM J. Sci. Comput. 20(3) (1999), 930-963 (electronic). [6] C. W. Gear and K. A. Gallivan, Automatic methods for highly oscillatory ordinary differential equations, Numerical Analysis (Dundee, 1981), pp. 115-124, Lecture Notes in Math., 912, Springer, Berlin-New York, 1982. [7] C. W. Gear and D. R. Wells, Multirate linear multistep methods, BIT 24(4) (1984), 484-502. [8] Ben Leimkuhler and Sebastian Reich, A reversible averaging integrator for multiple time-scale dynamics, J. Comput. Phys. 171(1) (2001), 95-114. [9] Mark Levi, Geometry and Physics of averaging with applications, Phys. D 132(1-2) (1999), 150-164. [10] Linda R. Petzold, An efficient numerical method for highly oscillatory ordinary differential equations, SIAM J. Numer. Anal. 18(3) (1981), 455-479. [11] E. Weinan and Bjorn Engquist, The heterogeneous multiscale methods, Comm. Math. Sci. 1(1) (2003), 87-132. [12] Mira Witt and C. Gorelik, Some historical aspects concerning the theory of dynamic systems. Dynamical Systems: A renewal of mechanism, S. Diner, D. Fargue and G. Lochak, eds., Singapore, World Scientific, 1933, pp. 250-262.

Keywords and phrases: dynamical system, kinematics, chaos.