PRELIMINARY ANALYSIS OF VARIATION OF PITCH MOTION OF A VEHICLE IN A SPACE ENVIRONMENT DUE TO FUEL SLOSHING IN A RECTANGULAR TANK

摘要

The equation of motion is derived for the angular rotation about the pitch axis of a space vehicle that is thrusting while partly filled with a liquid fuel that constitutes a large percentage of its mass. The forces due to thrust and rotation are of a magnitude equal to the capillary forces of the fluid and much greater than the Coriolis force. These forces are idealized to lie parallel to a longitudinal axis of the fluid tank. Changes in the angular rotation are generated by an impulsive torque applied to the vehicle. The fluid is considered to be irrotational, incompressible, inviscid, and contained in a rectangular tank.