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ABSTRACT

Physically based simulation of rigid body dynamics is commonly done by time-stepping systems forward in time. In this paper, we propose methods to allow time-stepping rigid body systems back-ward in time. Unfortunately, reverse-time integration of rigid bodies involving frictional contact is mathematically ill-posed, and can lack unique solutions. We instead propose time-reversed rigid body integrators that can sample possible solutions when unique ones do not exist. We also discuss challenges related to dissipation-related energy gain, sensitivity to initial conditions, stacking, constraints and articulation, rolling, sliding, skidding, bouncing, high angular velocities, rapid velocity growth from micro-collisions, and other problems encountered when going against the usual flow of time.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Physically based modeling

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.8 Types of Simulation
          Subjects: Animation

Keywords:
frictional contact, ill-posedness, inverse problems, linear complementarity, motion planning, rigid body dynamics