2006/07/31 by Ramses van Zon, Jeremy Schofield
Computer Science · Mathematics · Physics and Astronomy · #Block (permutation group theory) #Classical mechanics #Dynamics (music) #Equations of motion #Geometry #Integrator #Mathematical analysis #Mathematics #Modeling and Simulation Systems #Motion (physics) #Numerical methods for differential equations #Orientation (vector space) #Physics #Rigid body #Rigid body dynamics #Scientific Research and Discoveries #Symplectic geometry #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.jcp.2006.11.019
published as J. Comput. Phys. 225, 145-164 (2007) · Shortened paper with updated references, 28 pages, 3 figures
arxiv created 2006/12/18 · openalex publication_date 2007/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on initial conditions is explicit and the equations governing the orientation of the body involve only real numbers. Based on these results, an efficient method to calculate the location and orientation of the rigid body at arbitrary times is presented. This implementation can be used to verify the accuracy of numerical integration schemes for rigid bodies, to serve as a building block for event-driven discontinuous molecular dynamics simulations of general rigid bodies, and for constructing symplectic integrators for rigid body dynamics.