Solution of Euler's Equations of Motion and Eulerian Angles for near symmetric rigid bodies subject to constant moments
Abstract
Analytic expressions are found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant bodyfixed torques. These solutions provide the bodyfixed angular velocities and the attitude of the body, respectively, as functions of time. They are of special interest in applications to spinning spacecraft (such as the Galileo Spacecraft to be launched in 1984) because they include the effect of timevarying spin rate. Thus they can be applied to spinup and spindown maneuvers as well as to error analysis for thruster misalignments. The solutions are given for arbitrary initial conditions in terms of Fresnel, Sine and Cosine Integrals. Numerical integration of the governing differential equations has verified that the approximate analytic solutions are very accurate in many physical situations of interest.
 Publication:

American Institute of Aeronautics and Astronautics Conference
 Pub Date:
 August 1980
 Bibcode:
 1980aiaa.confT....L
 Keywords:

 Euler Equations Of Motion;
 Rigid Structures;
 Rotating Bodies;
 Spacecraft Motion;
 Angular Velocity;
 Galileo Spacecraft;
 Heuristic Methods;
 Integral Equations;
 Astrodynamics