DYNAMICS OF SWING OSCILLATORY MOTION IN HAMILTONIAN FORMALISM

Svetoslav Nikolov; Daniela Zaharieva

Scientific paper ID 1495 : 2017/3

DYNAMICS OF SWING OSCILLATORY MOTION IN HAMILTONIAN FORMALISM

Svetoslav Nikolov, Daniela Zaharieva

in this paper we apply hamiltonian formalism to the analysis of dynamical behavior of swing oscillatory motion. In the swing system, the swinger is modeled (idealized) as a rigid dumbbell with three point masses, three lengths, an angular position with vertical and an angular position relative to the ropes. Under these assumptions, for asymmetrical (all masses and lengths are different) and symmetrical (two masses and two lengths are equal) cases the hamiltonian is obtained. For the symmetrical case, we detect the existence of a homoclinic orbit and present the equation for it.

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динамика люлеещо се осцилиращо движение Хамилтонов формализъм хомоклинична орбитаdynamics swing oscillatory motion Hamiltonian formalism homoclinic orbitSvetoslav Nikolov Daniela Zaharieva

BIBLIOGRAPHY

[1] Whittaker E., A treatise on the analytical dynamics of particles and rigid bodies, Cambridge University Press, 1964.

[2] Arnold V., Mathematical methods in classical mechanics, Springer, Berlin, 1978.

[3] Guckenheimer J., Ph. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, NY, 1996.

[4] Panchev S., Theory of Chaos. Sofia, Bulgarian Acad. Press, 2001.

[5] Nikolov S., O. Wolkenhauer, J. Vera, Tumors as chaotic attractors, Molecular BioSystems, 10(2), pp. 172-179, 2014.

[6] Nikolov S., N. Nedkova, Gyrostat model regular and chaotic behaviour, J. of Theoretical and Applied Mechanics, 45(4), pp. 15-30, 2015.

[7] Sprott J., Elegant chaos. Algebraically simple chaotic flows, World Scientific, Singapore, 2010.

[8] Poincare H., Les methodes nouvelles de la mecanique celeste, vol. 1-3, Gauthier-Villars, 1892, 1893, 1899.

[9] Gelfreich V., D. Sharomov, Examples of Hamiltonian systems with transversal homoclinic orbits, Physics Letters A, 197, pp. 139-146, 1995.

[10] Gelfreich V., Splitting of small separatrix loop near the saddle-center bifurcation in area-preserving maps, Physica D, 136, 266-279, 2000.

[11] Case W., M. Swanson, The pumping of a swing from the seated position, American J. of Physics, 58, pp. 463-467, 1990.

[12] Wirkus S., R. Rand, A. Ruina, How to pump a swing, College Mathematics Journal, 29, pp. 266-275, 1998.

[13] Linge S., An assessment of swinger techniques for the playground swing oscillatory motion, Computer Methods in Biomechanics and Biomedical Engineering, 15(10), pp. 1103-1109, 2012.