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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:
70E17Motion of a rigid body with a fixed point
70K55Transition to stochasticity (chaotic behavior)
70Q05Control of mechanical systems (general mechanics)
93C10Nonlinear control systems
37N10Dynamical systems in fluid mechanics, oceanography and meteorology
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References:
[1] Moon, F. C.: Chaotic and fractal dynamics. (1992)
[2] Chen, G.; Dong, X.: From chaos to order: methodologies, perspectives and applications. (1998) · Zbl 0908.93005
[3] Kapitaniak, T.: Chaos for engineers: theory, applications and control. (1998) · Zbl 0904.58052
[4] Naschie, M. S. Ei: Introduction to chaos, information and diffusion in quantum physics. Chaos, solitons & fractals 7, 7-10 (1996)
[5] Kapitaniak, T.: Controlling chaotic oscillations without feedback. Chaos, solitons & fractals 2, 519-530 (1992) · Zbl 0759.34034
[6] Stefanski, A.; Kapitaniak, T.: Synchronization of two chaotic oscillators via a negative feedback mechanism. Chaos, solitons & fractals 40, 5175-5185 (2003) · Zbl 1060.70513
[7] Kapitaniak, T.: Continuous control and synchronization in chaotic systems. Chaos, solitons & fractals 6, 237-244 (1995) · Zbl 0976.93504
[8] Lakshmanan, M.; Murali, K.: Chaos in nonlinear oscillators: controlling and synchronization. (1996) · Zbl 0868.58058
[9] Chen, G.: Control and anticontrol of chaos. Ieee, 181-186 (1997)
[10] Chen, G.; Lai, D.: Anticontrol of chaos via feedback. Int. J. Bifurcat. chaos 8, 1585-1590 (1998) · Zbl 0941.93522
[11] Leimanis, E.: The general problem of the motion of coupled rigid bodies about a fixed point. (1965) · Zbl 0128.41606
[12] Leipnik, R. B.; Newton, T. A.: Double strange attractors in rigid body motion. Phys. lett. A 86, 63-67 (1981)
[13] Ge, Z. M.; Chen, H. K.; Chen, H. H.: The regular and chaotic motions of a symmetric heavy gyroscope with harmonic excitation. J. sound vib. 198, 131-147 (1996) · Zbl 1235.70016
[14] Ge, Z. M.; Chen, H. K.: Stability and chaotic motions of a symmetric heavy gyroscope. Jpn. J. Appl. phys. 35, 1954-1965 (1996)
[15] Tong, X.; Mrad, N.: Chaotic motion of a symmetric gyro subjected to a harmonic base excitation. Trans. ASME J. Appl. mech. 68, 681-684 (2001) · Zbl 1110.74711
[16] Chen, H. K.: Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping. J. sound. Vib. 255, 719-740 (2002) · Zbl 1237.70094
[17] Chen, H. K.; Lin, T. N.: Synchronization of chaotic symmetric gyros by one-way coupling conditions. Imeche J. Mech. eng. Sci. 217, 331-340 (2003)
[18] Lorenz, E. N.: Deterministic non-periodic flows. J. atmos. Sci. 20, 130-141 (1963)
[19] Rösler, O. E.: An equation for continuous chaos. Phys. lett. A 57, 397-398 (1976)
[20] Liu, W.; Chen, G.: A new chaotic system and its generation. Int. J. Bifurcat. chaos 13, 261-267 (2003) · Zbl 1078.37504
[21] Ueta, T.; Chen, G.: Bifurcation analysis of Chen’s system. Int. J. Bifurcat. chaos 10, 1917-1931 (2000) · Zbl 1090.37531