A Changing-Chart Symplectic Algorithm for Rigid Bodies and Other Hamiltonian Systems on Manifolds
SIAM Journal on Scientific Computing
Short Note: Reducing round-off errors in rigid body dynamics
Journal of Computational Physics
Algorithm 903: FRB--Fortran routines for the exact computation of free rigid body motions
ACM Transactions on Mathematical Software (TOMS)
Original article: Error growth in the numerical integration of periodic orbits
Mathematics and Computers in Simulation
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We compare several different second-order splitting algorithms for the asymmetric rigid body, with the aim of determining which one produces the smallest energy error for a given rigid body, namely, for given moments of inertia. The investigation is based on the analysis of the dominant term of the modified Hamiltonian and indicates that different algorithms can produce energy errors which differ by several orders of magnitude. As a byproduct of this analysis we remark that, for the special case of a flat rigid body with moments of inertia proportional to (1, 0.75, 0.25), one of the considered algorithms is in fact of order four.