Raman’s Billiard Ball Problem

2020 ◽  
pp. 109-115
Author(s):  
Partha Ghose ◽  
Dipankar Home
Keyword(s):  
Billiard Ball ◽  
Ball Problem

scholarly journals Glancing billiards

1982 ◽  
Vol 2 (3-4) ◽  
pp. 397-403 ◽  
Author(s):  
John N. Mather
Keyword(s):  
Bounded Region ◽  
Open Convex ◽  
Billiard Ball ◽  
Zero Curvature ◽  
Ball Problem

AbstractConsider the billiard ball problem in an open, convex, bounded region of the plane whose boundary is C2 and has at least one point of zero curvature. Then there are trajectories which come arbitrarily close to being positively tangent to the boundary and also come arbitrarily close to being negatively tangent to the boundary.

The elementary particle and the billiard ball

1966 ◽  
Vol 12 (2) ◽  
pp. 46
Author(s):  
Reginald O. Kapp
Keyword(s):  
Elementary Particle ◽  
Billiard Ball

Motion periodicity and bifurcation of a wave excited hopping ball

2019 ◽  
Vol 475 (2228) ◽  
pp. 20190137
Author(s):  
Gaurang Ruhela ◽  
Anirvan DasGupta
Keyword(s):  
Wave Amplitude ◽  
Harmonic Wave ◽  
Inelastic Collisions ◽  
Loss Of Stability ◽  
Elastic Surface ◽  
Minimum Frequency ◽  
Surface Motion ◽  
Return Map ◽  
Ball Problem ◽  
Subsequent Loss

We consider the problem of a hopping ball excited by a travelling harmonic wave on an elastic surface. The ball, considered as a particle, is assumed to interact with the surface through inelastic collisions. The surface motion due to the wave induces a horizontal drift in the ball. The problem is treated analytically under certain approximations. The phase space of the hopping motion is captured by constructing a phase-velocity return map. The fixed points of the return map and its compositions represent periodic hopping solutions. The linear stability of the obtained periodic solution is studied in detail. The minimum frequency for the onset of periodic hops, and the subsequent loss of stability at the bifurcation frequency, have been determined analytically. Interestingly, for small values of wave amplitude, the analytical solutions reveal striking similarities with the results of the classical bouncing ball problem.

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