Analytical Criterion for Chaotic Dynamics in Flexible Satellites with Nonlinear Controller Damping

Gray, Gary L.; Mazzoleni, Andre P.; Campbell, David R.

doi:10.2514/2.4294

Cited by 16 publications

(2 citation statements)

References 15 publications

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“…Papers in the latter field appear since the late 1970s and study conditions for chaotic behaviour in conventional feedback control systems (Mackey & Glass 1977;Baillieul et al 1980;Mareels & Bitmead 1986). Some recent results of such kind were reported for second-order systems (Alvarez et al 1997), for high-order systems with hysteresis (Postnikov 1998) and for mechanical control systems (Enikov & Stepan 1998;Gray et al 1998;Goodwine & Stepan 2000), to mention a few. A fruitful observation was made that the presence of chaos may facilitate control (Vincent & Yu 1991;Vincent 1997, see also Khryashchev 2004.…”

Section: (Iv) Chaos In Control Systemsmentioning

confidence: 99%

Control of chaos: methods and applications in mechanics

Fradkov

Evans

Andrievsky

2006

Phil. Trans. R. Soc. A.

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A survey of the field related to control of chaotic systems is presented. Several major branches of research that are discussed are feed-forward ('non-feedback') control (based on periodic excitation of the system), the 'Ott-Grebogi-Yorke method' (based on the linearization of the Poincaré map), the 'Pyragas method' (based on a time-delayed feedback), traditional for control-engineering methods including linear, nonlinear and adaptive control. Other areas of research such as control of distributed (spatio-temporal and delayed) systems, chaotic mixing are outlined. Applications to control of chaotic mechanical systems are discussed.

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Section: (Iv) Chaos In Control Systemsmentioning

confidence: 99%

Control of chaos: methods and applications in mechanics

Fradkov

Evans

Andrievsky

2006

Phil. Trans. R. Soc. A.

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“…Though our simulation had short episodes during which the nonlinear trajectory diverged slightly from the linear trajectory, it was subsequently attracted back to the linear trajectory. This behavior is quite characteristic of nonlinear dynamical systems with dissipation [ Gray et al , 1998; Chacon , 1999].…”

Section: Numerical Integrationmentioning

confidence: 99%

Forced obliquity variations of Mercury

Bills¹

2005

J. Geophys. Res.

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[1] The spin pole of Mercury is very nearly, but not quite, aligned with its orbit pole. Tidal dissipation has driven the free obliquity to very small values, and the high rate of spin pole precession allows the forced obliquity variations to remain small despite significant variations in orbital inclination and eccentricity. We present calculations of the obliquity for a 10 million year time span, centered on the present. The obliquity remains small, with typical values of 2-4 minutes of arc. The dominant period of obliquity oscillations is 895 kyr, which is also the main period at which the orbital inclination varies. If the orbit pole precession rate were uniform, dissipation would have driven Mercury into a Cassini state, in which the spin pole and orbit pole remain coplanar with the invariable pole, as the spin pole precesses about the moving orbit pole. However, due to the nonuniform orbit precession rate, this simple coplanar configuration is not maintained, except on a mode-by-mode basis. That is, when the orbit pole motion is represented as a sum of normal modes of the coupled oscillations of the planetary system, the spin pole coprecesses with the orbit pole at each modal frequency. This is a generalization of Cassini's second and third laws of lunar rotation to the case of nonuniform orbit precession. We compare results of a linearized obliquity model with a numerical integration of the equations of motion. The two solutions agree at the level of a few seconds of arc.

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