Norges Teknisk-naturvitenskapelige Universitet Efficient Time-symmetric Simulation of Torqued Rigid Bodies Using Jacobi Elliptic Functions

If the three moments of inertia are different from each other, the solution to the free rigid body (FRB) equations of motion is given in terms of Jacobi elliptic functions. Using the Arithmetic-Geometric mean algorithm, [1], these functions can be calculated efficiently and accurately. The overall approach yields a faster and more accurate numerical solution to the FRB equations compared to standard numerical ODE and symplectic solvers. This approach performs well also for mass asymmetric rigid bodies. In this paper we consider the case of rigid bodies subject to external forces. We consider a strategy similar to the symplectic splitting method proposed in [16]. The method here proposed is time-symmetric. We decompose the vector field of our problem in a FRB problem and another completely integrable vector field. In our experiments we observe that the overall numerical solution benefits greatly from the very accurate solution of the FRB problem. We apply the method to the simulation of artificial satellite attitude dynamics.