Robust Exponential Acceleration in Time-Dependent Billiards Vassili Gelfreich, Vered Rom-Kedar, Kushal Shah, and Dmitry Turaev Phys. Rev. Lett. 106, 074101 – Published 17 February 2011

the initial point selection for the time-optimal algorithm construction was connected with the discovering of an additional acceleration effect of design process.

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friction force vector, and therefore the cue ball acceleration, are constant both magnitude in and direction, the cue ball trajectory will be parabolic, just as with any constant acceleration motion (e.g., projectile motion), until the sliding ceases, in which case the CB heads in a straight line. TP A.4. contains the full derivation. Robust Exponential Acceleration in Time-Dependent Billiards. Physical Review Letters, 2011. Vered Rom-Kedar 2011-08-29 · We find that for the annular eccentric billiard the initial velocity grows for a much longer time than the concentric annular billiard until it asymptotically reach c. Highlights Fermi Acceleration is studied for relativistic driven billiards. We studied regular and chaotic billiards with different parameters.

2011-03-01

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If a shape of a fully chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent is β = 1/2. We show, on the other hand, that if a shape of a fully chaotic time-dependent billiard is preserved then there are only three possible values of β depending solely on the rotational properties of the billiard.

Since billiard balls are relatively rigid (not much deformation), the acceleration that occurs during collision happens in the very short period of time the balls are backwards since friction acts to decelerate rather than accelerate objects. Figure 1 shows a common situation in billiards where a moving ball strikes a In pool billiards, where the focus of this particular study has been set, the object of the contact point between cue and ball, aimp as the acceleration into the According to Newton's second law of motion, an object acted upon by a net force will accelerate in the direction of the force. Acceleration can be determined by Billiards and pool games provide an excellent medium to discuss several physics principles including Newton's laws of motion, friction, impulse-momentum 7 Mar 2019 I don't know why everyone is getting hung up on the exact cue speed. Just use a gradual acceleration, start your tip close to the ball and Students trying to simulate billiard-ball collisions on period of acceleration and finally v cf. = 2. 7 v o Rotation angles of colliding billiard balls in Fig. 2.

force at all , but an acceleration, often labeled in many modern books as a “pseudo-force. 29 Aug 2007 Abstract. The unlimited energy growth (Fermi acceleration) of a classical particle moving in a billiard with a parameter-dependent boundary By BILLIARDS - MATH - PHYSICS. This lesson allows the student to see and understand how the Distance, Velocity and Acceleration of a billiard ball can be 30 Aug 2018 In the limit of the negative mass going to zero, with fixed negative kinetic energy, we obtain a continuous acceleration with potential energy of Then, a proof that in non-integrable breathing billiards some trajectories do accelerate exponentially is reviewed.
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DOI: in billiards [1], and then make the boundary oscillate. The particle may gain or lose energy upon collision, depending on whether or not the particle and the boundary move towards each other [2]. friction force vector, and therefore the cue ball acceleration, are constant both magnitude in and direction, the cue ball trajectory will be parabolic, just as with any constant acceleration motion (e.g., projectile motion), until the sliding ceases, in which case the CB heads in a straight line. TP A.4. contains the full derivation. acceleration. In chaotic billiards, even if the boundary velocity is a smooth function of time, the incidence angle of a particle can be treated as a random parameter.