Maneuver analysis for spinning thrusting spacecraft and spinning tethered spacecraft
During axial thrusting of a spin-stabilized spacecraft undergoing orbital injections or control maneuvers, misalignments and center-of-mass offset create undesired body-fixed torques. The effects of the body-fixed torques, which in turn cause velocity pointing errors, can be reduced by ramping up (and then ramping down) the thruster. The first topic discussed in this thesis derives closed-form solutions for the angular velocity, Euler angles, inertial velocity, and inertial displacement solutions with nonzero initial conditions. Using the closed-form solutions, the effect of variations in the spin-axis moment of inertia and spin-rate on the spacecraft velocity pointing error are shown. The analytical solutions closely match numerical simulations. The next topic considers various ramp-up profiles (including parabolic, cosine, logarithmic, exponential, and cubic) to heuristically find a suboptimal solution to reduce the velocity pointing error. Some of the considered cosine, logarithmic, exponential, parabolic, and cubic profiles drive the velocity pointing error to nearly zero and hence qualify as effective solutions. The third topic examines a large tethered spacecraft that produces artificial gravity with the propulsion system on one end of the tether. Instead of thrusting through the center of mass, the offset thrust occurs at an angle to the tether which is held in the desired direction by changing the spin rate to compensate for decreasing propellant mass. The dynamics and control laws of the system are derived for constant, time-varying, planar, and non-planar thrust as well as spin-up maneuvers. The final topic discusses how the Bodewadt solution of a self-excited rigid body is unable to accurately predict the motion compared to a numerical integration of the equations of motion.
Longuski, Purdue University.
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