Ryotaro Sakamoto, University of Colorado Boulder; Daniel Scheeres, University of Colorado Boulder
Keywords: energy dissipation, finite element method, rigid body dynamics, debris
Abstract:
Solar radiation pressure leading to the Yarkovsky-OKeefeRadizievskii-Paddack (YORP) effect is considered to be one cause of changes in the rotational states of defunct geosynchronous earth orbit (GEO) satellites, in some cases taking them from uniform rotation to tumbling. For example, the transition of the rotational rates has been predicted and observed in the GOES 8 satellite [1]. This effect does not only affect defunct satellites, as the rotational rates of small asteroids are also changed by the YORP effect [2]. It has been predicted that internal energy dissipation is also an important component in the evolution of satellite spin states. Ideally, the kinetic energy is conserved without any additional torque for rigid body dynamics. In real life, friction between structural components or sloshing of internal liquid systems are considered as reasons for dissipation in space [3]. As a tumbling space craft loses energy, the state of the rotational rate approaches rotation along its maximum momentum inertia. In term of the three-dimensional dynamics, rotational rate along its maximum momentum inertia goes to a value based on minimum energy theory with the other rotational rates going to zero. One goal of this work is to find the relationship between energy dissipation and rotational rate for spinning defunct satellites and debris in general. In this research, we focus on the deformation of the satellite, which is one aspect of the energy dissipation. Deformational calculations are conducted using a finite element analysis of a flexible satellite model. The detailed finite element model captures the behavior of internal variations of the position of the nodes, their velocity and the total system kinetic energy. Time vary accelerations are applied using a tumbling satellite model. By combing the finite element analysis and rigid body dynamics, including the deformation effects, the energy transition in the spin state is modeled and revealed.
Our three-dimensional model is composed of a simple solar array and body component using a finite element model. To evaluate the energy transition, the kinetic energy is compared among two situations of dynamics. One is simple rigid body dynamics with constant inertia matrix, and this is taken as the nominal results. Another situation of the dynamics has time varying inertia matrix caused by deformation, which is modeled by finite element analysis. For the sequence of the simulation, at first, a constant rotation rate which models tumbling is applied to the rigid body dynamics. Then this updated rotational rate is taken into the finite element dynamics and deformation is calculated. Finally, based on these deformation parameters, the time varying inertia matrix is established. This updated matrix makes the difference of the kinetic energy with nominal simulation, that is the amount of the energy dissipation. These simulations will be compared with the observation data for the tumbling satellite GOES-8 [1] to develop estimates of what appropriate level of dissipation should be used in our simulations for this particular asteroid.
[1] Albuja A. A., Scheeres, D. J., Cognion, R. L., Ryan, W., Ryan, E. V., The YORP effect on the GOES 8 and GOES 10 satellites: A case study, Advances in Space Research, Vol. 61, pp. 122-144, 2018.
[2] Lowry, S., et al., Direct detection of the asteroidal YORP effect, Science, Vol. 316, pp. 272-274, 2007.
[3] Kojima, Y., Taniwaki, S., and Okami, Y., Dynamic simulation of stick-slip motion of a flexible solar array, Control Engineering Practice, Vol. 16, 2008, pp. 724-735.
Date of Conference: September 17-20, 2019
Track: Astrodynamics