Annihilation of Transverse Velocity Bias During Spinning-Up Maneuvers

Abstract

During spinning-up maneuvers of a spacecraft, the spin thrusters can produce a e nite transverse velocity offset or bias in the plane perpendicular to the spin axis. A two-burn scheme is introduced to eliminate this offset. The fundamental transcendental equation for the two-burn scheme is of the same form as Kepler' s equation. The relationship between the transcendental equation and Kepler' s equation is investigated. Numerical results demonstrate the effectiveness of the two-burn scheme. scribe the spin-rate-control e ight algorithm that is used both to alter and to maintain spin rate. The problem is challenging because the thruster causes body-e xed torques about three axes and body-e xed forces along two axes. In this paper, a maneuver scheme is presented that annihilates the transverse velocity bias accrued during spinning-up maneuvers. This offset velocity is directly dependent on the unbalanced force of the spinup thrusters and so is particularly noticeable if there is a large thruster couple mismatch or if (as in the case of the Galileo spacecraft)thereisonlyonespinupthruster (i.e.,nocoupleavailable as depicted in Fig. 1 ). The maneuver scheme consists of two burns with a coast period in between. The initial burn angle is given by a transcendental equation similar to Kepler' s equation. However, in contrast to Kepler' s equation, which has a unique solution for a given eccentricity, the transcendental velocity equation can have an ine nite number of solutions. (The fact that there are close analogies between the classic problem of rigid-body motion and the orbital motion of two bodies is notnew— it has been noted in an interesting paper by Cochran et al. 2 ) OurproblemisrelatedtothatdiscussedbyLonguskietal., 3 where a two-burn scheme is introduced to annihilate angular momentum bias due to transverse torques during a spinning-up maneuver. We consider the problem of transverse velocity accumulation due to transverse forces, which is not addressed in Ref. 3. Our approach makesuseoftheanalytical approximation 4 for velocityaccrued due toappliedforcesina spinupmaneuver.Theresulting transcendental equationisdifferentfromthatofRef.3butiscloselyrelated.Finally, we investigate the existence of multiple solutions for the two-burn scheme.