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Creators/Authors contains: "Yeun_Kim, Ki"

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  1. ; ; (, Nonlinearity)
    Abstract We consider billiards with cusps and with gravity pulling the particle into the cusp. We discover an adiabatic invariant in this context; it turns out that the invariant is in form almost identical to the Clairaut integral (angular momentum) for surfaces of revolution. We also approximate the bouncing motion of a particle near a cusp by smooth motion governed by a differential equation—which turns out to be identical to the differential equation governing geodesic motion on a surface of revolution. We also show that even in the presence of gravity pulling into a cusp of a billiard table, only the direct-hit orbit reaches the tip of the cusp. Finally, we provide an estimate of the maximal depth to which a particle penetrates the cusp before being ejected from it. 
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