1999/01/17 by I. P. Omelyan, Igor P. Omelyan, Omelyan, Igor P.
Engineering · Physics and Astronomy · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Mechanics and Biomechanics Studies #physics.chem-ph #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.physics/9901024
27 pages, 2 figures; submitted to J. Comput. Phys
openalex publication_date 1999/01/17 · arxiv created 1999/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration, whereas orientational positions are expressed in terms of either principal axes or quaternions. As a result, the rigidness of molecules appears to be an integral of motion, despite the atom trajectories are evaluated approximately. The algorithm derived is free of any iterative procedures and it allows to perform both energy- and temperature-conserving simulations. The corresponding integrators are time reversible but the symplectic behaviour is only achieved in mean. Symplectic versions are also described. The provide the conservation of volume in phase space precisely at each time step and, moreover, lead to exact solutions for angular velocities in the inertial-motion regime. It is shown that the algorithm exhibits excellent stability properties and conserves the energy even somewhat better than the atomic-constraint technique.