Attitude Motion of Cylinder in Variable Electrostatic Field Near Libration Point

Abstract

This paper explores the spatial attitude motion of an electrostatic cylindrical container (E container) in a variable attracting electrostatic field. This field generated by the E container and the orbiting spacecraft (orbiter) located at the L1 libration point of the Mars–Phobos system is used to capture the E container by the orbiter in the Phobos Sample Return mission. Based on the Lagrange formalism and using the Euler angles, the equations of attitude motion of a cylindrical E container are constructed in the framework of the circular restricted three-body problem with the addition of the electrostatic force and torque acting on the E container. For modeling electrostatic force and torque acting on a cylindrical E container, the multisphere method is used, which was developed by Stevenson and Schaub (Multi-Sphere Method for Modeling Electrostatic Forces and Torques,” Advances in Space Research, Vol. 51, No. 1, 2013, pp. 10–20). The influence of gravitational, centrifugal, and electrostatic moments on angular motion for different initial conditions has been studied analytically by analyzing the equations of both attitude motion and numerical simulations. It is shown that the action of the aforementioned torques as the E container approaches the orbiter causes the excitation of high-frequency nutation oscillations with large amplitudes. On the other hand, there are no natural and artificial factors of physical nature that could lead to damping of oscillations of large amplitude, and this fact corresponds to the obtained equations of attitude motion. Also, the electrostatic torque is the greatest contributor to the oscillations with large amplitude. Hence, it is clear that the E container must have a spherical current-conducting shell: in which case, the electrostatic torque turns to zero.