Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Aslanov V. S., Ivanov B. V. Chaotic Motion of Nonlinear System. Izv. Sarat. Univ. Math. Mech. Inform., 2008, vol. 8, iss. 4, pp. 38-43. DOI: 10.18500/1816-9791-2008-8-4-38-43

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531.36: 534.1

Chaotic Motion of Nonlinear System

Aslanov Vladimir Stepanovich, Samara National Research University, Russia
Ivanov Boris Vsevolodovich, Samara National Research University, Russia

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.

  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.