Cite this article as:

Aslanov V. S., Ivanov B. V. Chaotic Motion of Nonlinear System. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2008, vol. 8, iss. 4, pp. 38-43. DOI: https://doi.org/10.18500/1816-9791-2008-8-4-38-43

Language: 
Russian
Heading: 
Mechanics
UDC: 
531.36: 534.1

Chaotic Motion of Nonlinear System

Authors: 
Aslanov Vladimir Stepanovich, Samara National Research University, 34, Moskovskoye Shosse, Samara, 443086, Russia , aslanov_vs@mail.ru
Ivanov Boris Vsevolodovich, Samara National Research University, 34, Moskovskoye Shosse, Samara, 443086, Russia , boris063@mail.ru
Abstract: 

Chaotic motion of a body of the blunted form in an atmosphere described is considered by the nonlinear differential equation of the second order. On a body the restoring moment, the small perturbed periodic moment and the damped moment operates. The phase portrait of the unperturbed system has points of unstable balance. On the basis of Melnikov method the criteria determining borders of chaos of system are found. The results of the numerical simulations confirming validity, received criterion are submitted.

Key words: 
nonlinear system, periodic perturbations, chaos, heteroclinic orbits, Melnikov method
DOI: 
https://doi.org/10.18500/1816-9791-2008-8-4-38-43
References

1. Асланов В.С. Пространственное движение тела при спуске в атмосфере. М.: Физматлит, 2004.

2. Ярошевский В.А. Движение неуправляемого тела в атмосфере. М.: Машиностроение, 1978.

3. Мельников В.К. Об устойчивости центра при периодических по времени возмущениях // Тр. Моск. мат. об-ва. 1963. Т. 12. С. 1–56.

4. Wiggins S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. N.Y.: Springer, 1990. 

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