International Journal of Theoretical Physics

, Volume 35, Issue 1, pp 189–198 | Cite as

Classical irreversibility and mapping of the isosceles triangle billiard

  • Richard L. Liboff


Mapping of the two-dimensional isosceles triangle billiard onto the circular one-dimensional motion of two mass points is described. The singular nature of trajectories directly incident on an acute vertex is discussed in the framework of the present mapping. For an obtuse-angled isosceles triangle, dynamical equations in two-particle space applied to an orbit along a hypotenuse incident on the obtuse vertex suggests irreversible behavior at the critical angle ψ=2π/3. Thus it is found that the nonsingular motion of a finite smooth-walled disk on this trajectory exhibits irreversibility. A finite spherical smooth-walled particle moving in a uniform right cylinder whose cross section includes this critical vertex angle likewise exhibits irreversibility. Each such example comprises an irreversible orbit for a single-particle Hamiltonian.


Field Theory Elementary Particle Quantum Field Theory Dynamical Equation Mass Point 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Richard L. Liboff
    • 1
  1. 1.Schools of Electrical Engineering and Applied Physics and Center for Applied MathematicsCornell UniversityIthaca

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