хаос

On the Complex Dynamics in Simplest Vibrational Systems with Hereditary-Type Friction

Authors: Igumnov L. A., Metrikin V. S.

The dynamics of a number of vibrational systems, accounting for the forces of hereditary-type dry friction and a vibration limiter, are studied in the paper. The interaction between the vibration limiter and the vibrational system is assumed to obey Newton's hypothesis. A general mathematical model has been developed, which is a strongly nonlinear non-autonomous system with a variable structure. The dynamics of the mathematical model is studied numerically-analytically, using the mathematical apparatus of the point mapping method.

Chaotic Motion of Nonlinear System

Authors: Aslanov V. S., Ivanov B. V.

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.

Chaotic motion of top with displaced mass center

Authors: Losyakova D. A.

 The motion of solid body with a small displacement mass center from the axis of dynamic symmetry has been studied. Analytical conditions for the existence of a hyperbolic singular point in the phase portrait of the system and the analytical solution for the separatrices have been obtained. Body makes a chaotic motion near separatrices under the influence of small perturbations caused by the asymmetry of the body.