Chaotic Attitude Motion of Satellites Under Small Perturbation Torques

On the Chaotic Instability of a Nonsliding Liquid-Filled Top with a Small Spheroidal Base via Melnikov-Holmes-Marsden Integrals

“…, t k9 for k = x, y, z are defined in Appendix A. Similar to Kuang et al [24], one may transform Eulerian Equations (35) in association with (56) and Poisson's Equations (5) into the disturbed Hamiltonian equations in terms of the Deprit variables as mentioned in the last section. In order to develop a criterion for the judgment of the onset of chaotic dynamics of the periodically perturbed liquid-filled top rolling without sliding on the rough horizontal plane we are required to compute the real zeros of the MHM integral based on the heteroclinic orbits of the disturbed liquid-filled top.…”

“…[24,[26][27][28][29], Leung and Kuang [30], Mielke and Holmes [31], Tong et al [32,33], Koiller [34], and Ziglin [35] amongst many others. Based on the work of Wiggins and Shaw [36], Kuang et al [24,26] obtained the Melnikov integral of chaotic rotational dynamics of the gyrostat under the action of small perturbation torques, in the form of damping torques plus periodic moments. Certain interesting models on the nonlinear dynamics of dynamical systems may be found in Wittenburg [37], Heijden and Thompson [38], Thompson and Stewart [39], Hagedorn [40], Chen and Leung [41], and Davies and Moon [42] amongst others.…”

“…Applications of the MHM integrals on a variety of mechanical systems have been carried out by Kozlov [5], Kuang et al. [24,[26][27][28][29], Leung and Kuang [30], Mielke and Holmes [31], Tong et al [32,33], Koiller [34], and Ziglin [35] amongst many others. Based on the work of Wiggins and Shaw [36], Kuang et al [24,26] obtained the Melnikov integral of chaotic rotational dynamics of the gyrostat under the action of small perturbation torques, in the form of damping torques plus periodic moments.…”

“…The generalized Deprit variables in Equations (42) are functions of time t only. The physical meaning of the original Deprit variables L , G, H, l, g, and h may be found in Kuang et al[24]. The relations between the direction cosines and Deprit variables are, γ x = (sin I sin g) cos l + (cos I sin b + sin I cos b cos g) sin l, γ y = −(sin I sin g) sin l + (cos I sin b + sin I cos b cos g) cos l,…”

Control and Synchronization Chaotic Satellite using Active Control

“…As space technology progresses, the need for improved satellite systems by better understanding of satellite dynamics has continuously kept attention [20].Recently, nonlinear dynamics, especially the chaotic attitude dynamics of a satellite have attracted the attention of many scientists [21,22].The control of the Slave satellite, on the other hand, is a synchronization problem. .…”