A method for approximating the vacuum motions of spinning rigid symmetrical bodies with varying spin rates and inertias has been completed. The analysis includes the effects of time varying thrust misalinements, mass unbalance, and jet damping. Results are given in the form of equations for space-referenced Euler angles, flight-path angles, body-referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. The method consists of dividing the problem into intervals during which the time-dependent variables are assumed constant at their mean interval value. In order to check this procedure, solutions for various interval sizes are compared with solutions obtained with numerical methods. Although the method is somewhat lengthy for accurate hand computation in most cases, it is readily programed for machine solutions.
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