Ulrich Mutze
Precision-dependent symmetry breaking in simulated motion of polyspherical grains
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ABSTRACT. A system of 10 elastic polyspherical particles, initially falling freely in the interior of a spherical cavity is simulated employing a time-stepping method and a time-stepping rate which exhibit excellent conservation of total energy. The particles are initially at rest and placed mirror-symmetrically with respect to a vertical plane that divides the spherical cavity into two halves. From the equations of mechanics it follows that this initial mirror symmetry also holds for all future states, despite the many collisions that may have happened. Accumulation of rounding errors actually destroys this behavior in a numerical simulation. This is shown by doing the computation with numerical precision 16, 20, 30, and 40.