Session
Frank J. Redd Student Competition
Location
Salt Palace Convention Center, Salt Lake City, UT
Abstract
Passive magnetic attitude control (PMAC) systems are selected for integration in CubeSat designs on account of their simplicity and lack of power consumption. These systems function by simultaneously dissipating a satellite’s rotational kinetic energy as heat and orienting it according to the Earth’s magnetic field. This process is critical for establishing steady-state attitude, a stable rotational state required for conducting mission operations and enabling downlink to ground stations. Comprehensive attitude simulations are necessary for confirming the reliability of a PMAC system to provide timely attitude convergence for a wide range of deployment velocities and orientations. An attitude damping phase precedes steady-state, and the duration may last weeks or longer. As simulation timespans of at least one month are required to prove a stable convergence, standard adaptive Runge-Kutta (4, 5) solvers (RK45) are less suitable because of the accumulation of numerical error. Lie group variational integrators (LGVIs) offer a compelling alternative. LGVIs demonstrate excellent geometric conservation properties and maintain attitude matrix orthogonality, resulting in improved physical accuracy. A three-step validation chain is followed to verify a developed LGVI-based attitude simulator, comprising validations against literature, a cross-framework verification with an RK45-based simulator, and an invariant-preservation analysis. In a torque-free scenario, the LGVI is found to maintain a relative angular momentum error on the order of 10-13 while halving the runtime of an RK45 integrator configured with a comparable timestep. The validated LGVI simulator is employed to model the performance of eight PMAC configurations for the Get Away Special Radio and Antenna Transparency Satellite in a 1,001-trial Monte Carlo analysis. The results inform the final design recommendation of a four-rod, 1.5U configuration and indicate the unexpectedly poor damping performance of 1U configurations. It is determined that this phenomenon is associated with inertial symmetry that limits the transfer of rotational kinetic energy between body axes.
Document Type
Event
Validated Lie Group Variational Integrator-Based Simulator for Passive Magnetic Attitude Control of the GASRATS CubeSat
Salt Palace Convention Center, Salt Lake City, UT
Passive magnetic attitude control (PMAC) systems are selected for integration in CubeSat designs on account of their simplicity and lack of power consumption. These systems function by simultaneously dissipating a satellite’s rotational kinetic energy as heat and orienting it according to the Earth’s magnetic field. This process is critical for establishing steady-state attitude, a stable rotational state required for conducting mission operations and enabling downlink to ground stations. Comprehensive attitude simulations are necessary for confirming the reliability of a PMAC system to provide timely attitude convergence for a wide range of deployment velocities and orientations. An attitude damping phase precedes steady-state, and the duration may last weeks or longer. As simulation timespans of at least one month are required to prove a stable convergence, standard adaptive Runge-Kutta (4, 5) solvers (RK45) are less suitable because of the accumulation of numerical error. Lie group variational integrators (LGVIs) offer a compelling alternative. LGVIs demonstrate excellent geometric conservation properties and maintain attitude matrix orthogonality, resulting in improved physical accuracy. A three-step validation chain is followed to verify a developed LGVI-based attitude simulator, comprising validations against literature, a cross-framework verification with an RK45-based simulator, and an invariant-preservation analysis. In a torque-free scenario, the LGVI is found to maintain a relative angular momentum error on the order of 10-13 while halving the runtime of an RK45 integrator configured with a comparable timestep. The validated LGVI simulator is employed to model the performance of eight PMAC configurations for the Get Away Special Radio and Antenna Transparency Satellite in a 1,001-trial Monte Carlo analysis. The results inform the final design recommendation of a four-rod, 1.5U configuration and indicate the unexpectedly poor damping performance of 1U configurations. It is determined that this phenomenon is associated with inertial symmetry that limits the transfer of rotational kinetic energy between body axes.
