Determination of the Chaos Onset in Mechanical Systems with Several Equilibrium Positions |
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Authors: | Yuri V Mikhlin Gayane V Manucharyan |
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Institution: | (1) Department of Applied Mathematics, National Technical University “Kharkov Polytechnical Institute”, 21 Frunze str., Kharkov, 61002, Ukraine |
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Abstract: | Determination of the chaos onset in some mechanical systems with several equilibrium positions are analyzed. Namely, the snap-through
truss and the oscillator with a nonlinear dissipation force, under the external periodical excitation, are considered. Two
approaches are used for the chaos onset determination. First, Padé and quasi-Padé approximants are used to construct closed
homoclinic trajectories for a case of small dissipation. Convergence condition used earlier in the theory of nonlinear normal
vibration modes as well conditions at infinity make possible to evaluate initial amplitude values for the trajectories with
admissible precision. Mutual instability of phase trajectories is used as criterion of chaotic behavior in nonlinear systems
for a case of not small dissipation. The numerical realization of the Lyapunov stability definition gives us a possibility
to observe a process of appearance and fast enlargement of the chaotic behavior regions if some selected parameters of the
dynamical systems under consideration are changing. |
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Keywords: | Padé approximants Homoclinic orbits Mutual unstability |
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