DYNAMICS OF A DOUBLE PENDULUM

Svetoslav Nikolov

Scientific paper ID 2238 : 2022/3

DYNAMICS OF A DOUBLE PENDULUM

Svetoslav Nikolov

In this paper we consider the motion of the double pendulum attached to a platform that has a prescribed vertical oscillation relative to an inertial frame in Hamiltonian context. In order to investigate the dynamics of the system, we obtain its Hamiltonian which has unperturbed and perturbed parts. Thus, some analytical and numerical results about dynamics of the system are obtained.

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двойно махало aнализ неавтономен Хамилтонианdouble pendulum analysis nonautonomous HamiltonianSvetoslav Nikolov

BIBLIOGRAPHY

[1] Nayfeh, A., Mook, D., Nonlinear oscillations, John Wiley & Sons, NY, 1995.

[2] Guckenheimer, J., Holmes, Ph., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, vol. 42, Springer Science & Business Media, 2013.

[3] Baker, G., Blackburn, J., The pendulum: a case study in physics, Oxford University Press, NY, 2005.

[4] Dutra, M., de Pina Filho, A., Romano, V., Modeling of a bipedal locomotor using coupled nonlinear oscillators of Vann der Pol, Biological Cybernetics, vol. 88, pp. 286-292, 2003.

[5] Nikolov, S., Vassilev, V., Zaharieva, D., Analysis of swing oscillatory motion, Studies in Computational Intelligence, In: Advanced Computing in Industrial Mathematics: 13th Annual Meeting of the Bulgarian Section of SIAM, Springer Nature, pp. 313-323, 2021.

[6] Nikolov, S., Zaharieva, D., Dynamical behaviour of compound elastic pendulum, MATEC Web of Conferences, vol. 145, art. No 01003, 2018.

[6] Arnold, V., Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, NY, 1988.

[7] Richter, P., Scholz, H.-J., Chaos in classical mechanics: the double pendulum, In: Stochastic Phenomena and Chaotic Behaviour in Complex Systems (P. Schuster, ed.), Springer-Verlag, Berlin, pp. 86–97, 1984.

[8] Hsu, C., Cheng, W., Applications of the theory of impulsive excitation and new treatments of general parametric excitation problems, J. Appl. Mech., vol. 40(1), pp. 78-86, 1973.

[9] Treschev, D., Zubelevich, O., Introduction to the perturbation theory of Hamiltonian systems, Springer-Verlag, Berlin, 2010.

[10] Bogolyubov, N., Mitropol`skii Yu., Asymptotic methods in the theory of non-linear oscillations, Gordon and Breach, NY, 1961.

[11] Nekhoroshev, N., An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems, Uspekhi Mat. Nauk, vol. 32(6(198)), pp. 5–66,1977.

[12] Wiggins, S., Global bifurcations and chaos. Analytical methods. Springer-Verlag, NY, 1988.