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UBC Theses and Dissertations

Dynamics of single and multibody earth orbiting systems Sharma, Subhash Chander


The thesis aims at studying the dynamics of single and multibody systems with a variety of spacecraft oriented applications including configuration control for an instrumentation payload deployed from a spacecraft, the Solar Satellite Power Station (SSPS), a Space Shuttle supported tethered payload, etc. The problem is approached in an increasing order of complexity. In the beginning librational dynamics and force distribution for an axisymmetric, gravity oriented, rigid configuration are considered. The governing nonlinear, nonautonomous and coupled equations of motion are analyzed using Butenin's variation of parameter approach in conjunction with the Poincare-type expansion method, and the validity of the solutions established through numerical integration. The closed-form character of the solutions proved useful in identifying periodic solutions and resonance characteristics of the system. Furthermore, they provided considerable insight into the system behaviour over a range of the orbital eccentricity, inertia parameter and initial disturbances. Application of the analysis is demonstrated through the Gravity Gradient Test Satellite (GGTS). Next, general equations of librational motion, force and moment are derived for an arbitrarily-shaped, rigid spacecraft and approximate closed-form solutions obtained for spinning and gravity oriented systems using the Poincare-type analysis. The approach yields useful information concerning response to external disturbances as affected by the system parameters. The method is applied to several configurations: Explorer XX, an instrument package deployed from the Space Shuttle and the SSPS. Finally, a general dynamical formulation for a triaxial multibody system, in a circular orbit, with an elastic interconnecting link in the form of a tether or a beam is developed. The highly complicated coupled, nonlinear, nonautonomous equations of motion are linearized and their exact solution presented. Also expressions for forces and moments required to orient an object in space are obtained. This analytical procedure is applied to several configurations of practical interest. Throughout, the emphasis is on evolving a general formulation of the problem and its acceptable solution. Numerical results are presented only to appreciate significant response characteristics of the system. The general character of the analysis should prove useful in studying the dynamics of a wide range of existing and future spacecraft.

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