Symplectic algorithms for simulations of rigid body systems using the exact solution of free motion

摘要

Elegant integration schemes of second and fourth order for simulations ofrigid body systems are presented which treat translational and rotationalmotion on the same footing. This is made possible by a recent implementation ofthe exact solution of free rigid body motion. The two schemes aretime-reversible, symplectic, and exactly respect conservation principles forboth the total linear and angular momentum vectors. Simulations of simple testsystems show that the second order scheme is stable and conserves all constantsof the motion to high precision. Furthermore, the schemes are demonstrated tobe more accurate and efficient than existing methods, except for highdensities, in which case the second order scheme performs at least as well,showing their general applicability. Finally, it is demonstrated that thefourth order scheme is more efficient than the second order scheme provided thetime step is smaller than a system-dependent threshold value.