A ball moves freely on the surface of a round billiard table, and undergoes elastic reflections at the boundary of the table. The motion is frictionless, and once started it continues indefinitely. The initial conditions are that the ball starts at a point A on the boundary and that the chord AB drawn in the direction of the initial velocity subtends an angle a at the centre O of the table. Discuss the dependence of the trajectory of the ball on a.
A ball moves freely on the surface of a round billiard table, and undergoes elastic reflections at the boundary of the table. The motion is frictionless, and once started it continues indefinitely. The initial conditions are that the ball starts at a point A on the boundary and that the chord AB drawn in the direction of the initial velocity subtends an angle a at the centre O of the table. Discuss the dependence of the trajectory of the ball on a.
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Transcribed Image Text:A ball moves freely on the surface of a round billiard
table, and undergoes elastic reflections at the boundary
of the table. The motion is frictionless, and once started
it continues indefinitely. The initial conditions are that
the ball starts at a point A on the boundary and that the
chord AB drawn in the direction of the initial velocity
subtends an angle a at the centre O of the table. Discuss
the dependence of the trajectory of the ball on a.
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