Geodesic
Chaotic motion of nonlinear system
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 38-43.

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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. 
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V. S. Aslanov; B. V. Ivanov. Chaotic motion of nonlinear system. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 38-43. http://geodesic.mathdoc.fr/item/ISU_2008_8_4_a5/

[1] Aslanov V. S., Prostranstvennoe dvizhenie tela pri spuske v atmosfere, Fizmatlit, M., 2004

[2] Yaroshevskii V. A., Dvizhenie neupravlyaemogo tela v atmosfere, Mashinostroenie, M., 1978

[3] Melnikov V. K., “Ob ustoichivosti tsentra pri periodicheskikh po vremeni vozmuscheniyakh”, Tr. Mosk. mat. ob-va, 12, 1963, 1–56 | Zbl

[4] Wiggins S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, N.Y., 1990 | MR