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Anti-control of chaos in rigid body motion. (English) Zbl 1046.70005

Summary: Anti-control of chaos for a rigid body has been studied in the paper. For certain feedback gains, a rigid body can easily generate chaotic motion. Basic dynamical behaviors, such as symmetry, invariance, dissipativity and existence of attractor, are also discussed. The transient behaviors of the chaotic system have also been presented as the feedback gain changed. Of particular interesting is the fact that the chaotic system can generate a complex multi-scroll chaotic attractor under the appropriate feedback gains. Finally, it was shown that the system could be related to the famous Lorenz equations and Chen system. In other words, the system can easily display all the dynamical behaviors of the famous Lorenz equations and Chen system.

MSC:

70E17 Motion of a rigid body with a fixed point
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
70Q05 Control of mechanical systems
93C10 Nonlinear systems in control theory
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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References:

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