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AN IMPLICIT TIME‐STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION
Author(s) -
STEWART D. E.,
TRINKLE J. C.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960815)39:15<2673::aid-nme972>3.0.co;2-i
Subject(s) - time stepping , coulomb , coulomb friction , rigid body , spinning , collision response , convergence (economics) , inelastic collision , classical mechanics , rigid body dynamics , dynamics (music) , point (geometry) , physics , mechanics , mathematics , mathematical analysis , computer science , geometry , collision , engineering , mechanical engineering , nonlinear system , computer security , acoustics , quantum mechanics , electron , collision detection , economic growth , discretization , economics
In this paper a new time‐stepping method for simulating systems of rigid bodies is given which incorporates Coulomb friction and inelastic impacts and shocks. Unlike other methods which take an instantaneous point of view, this method does not need to identify explicitly impulsive forces. Instead, the treatment is similar to that of J. J. Moreau and Monteiro‐Marques, except that the numerical formulation used here ensures that there is no inter‐penetration of rigid bodies, unlike their velocity‐based formulation. Numerical results are given for the method presented here for a spinning rod impacting a table in two dimensions, and a system of four balls colliding on a table in a fully three‐dimensional way. These numerical results also show the practicality of the method, and convergence of the method as the step size becomes small.