Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1999; 36(2): 403-419

Printed March 1, 1999

Copyright © The Korean Mathematical Society.

Linear stability of a periodic orbit of two-ball linear systems

Dong-Pyo Chi and Sunbok Seo

Abstract

We introduce a Hamiltonian system which consists of two balls in the vertical line
colliding elastically with each other and the floor. Wojtkowski proved that for the
system of two linear balls with a linear potential (with gravity), there is a periodic
orbit which becomes linearly stable if $m_1 particle and $m_2$ is that of an upper particle.
For our system having a quadratic potential, we find an appropriate coordinate to
obtain symplectic collision maps, obtain a periodic orbit and prove conclusively
that the periodic orbit is linearly stable without the mass condition.

Keywords: system of falling balls, symplectic map, collision map, linear stability of a periodic orbit

MSC numbers: 70F35

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