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D. G. Korycansky (CODEP/IGPP University of California Santa Cruz)
I present a scheme for simulating the orbital dynamics of collections of self-gravitating rigid bodies. The goal is to model the dynamics of asteroids, for example, the formation of asteroid binaries and gravitational aggregates. The bodies are modeled as polyhedra of general shapes with an arbitary number of triangular faces. The gravitational potentials are calculated using the ``polyhedron gravity'' scheme of Werner and Scheeres. Mutual forces and torques are calculated via surface integrals done by quadrature. Additional components of the overall scheme include updating the spin vector and orientation of the bodies, and their positions, velocities, and angular momenta after each timestep. Collisions are allowed, and treated via the impulse approximation. Inelastic or frictional collisions can be handled via coefficients of restitution. Collisions are detected by checking if body vertices or edges have penetrated body faces among pairs of objects. Conservation tests of total linear and angular momentum, and total energy, give quite satisfactory results, in general, though high-order quadratures, large numbers of polyhedra faces, or small timesteps may be required if very good conservation is required. Also, at present, the collision-detection scheme occasionally yields ``bad'' collisions due to the discrete timestep. While a timestep bisection process usually resolves the problem (which is also mitigated by taking smaller timesteps), improvement is needed here.
This research was supported by NASA grant NAG5-11521-001.
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.