Dynamic modeling and analysis of a flexible sailcraft

Abstract

The coupled orbit, attitude and structural dynamics is very important for an orbiting sailcraft because the orbit is determined by the attitude, and the attitude and structural vibrations are affected mutually. Thus it is critical to derive the coupled dynamics and analyze how the vibrations are excited by the attitude motions, and how the orbit and attitude motions are affected by the vibrations. To solve this problem, the coupled orbit, attitude and structural dynamics is established for the sailcraft modeled by the Euler beam with large deformations merely experiencing the pitch motion in this paper. The Von-Karman’s nonlinear strain-displacement relation is adopted to consider the sailcraft with large transverse deformations, moderate rotations and small strains. The external loads include the torques by the control vanes, the offset between the center-of-mass (cm) and center-of-pressure (cp) and the gravity gradient force. The full nonlinear coupled dynamics denoted by “model 1” is established using Lagrange equation method based on the calculation of the kinetic energy, strain energy, the dissipation function and the external loads respectively. “model 2, 3” are obtained by neglecting the geometrically nonlinear terms, the second and higher terms including the vibration displacement, velocity and acceleration in “model 1” respectively, and “model 4” is a rigid body model. A 90deg pitch maneuver will be performed for the sailcraft initially on the geostationary (GEO) orbit for all the four models. The control torque generated by the control vanes is obtained based on the nonlinear optimal proportional–integral controller considering the saturation problem of the control vanes. The attitude, orbit and vibration responses are presented and compared to see the differences between the four models, some discussions and conclusions on the dynamics and control are also given, all based on the dynamics simulations.