[DEMONSTRATION] - Two-Dimensional Colliding Pendulums скачать в хорошем качестве

[DEMONSTRATION] - Two-Dimensional Colliding Pendulums

Two identical billiard-ball pendulums touch side-by-side in equilibrium. The balls are pulled aside a small amount in the transverse direction, and one ball is given a velocity directly toward the other ball, which is initially at rest. Repeated collisions occur, where one ball undergoes uniform circular motion (conical pendulum) over a half-cycle, and the other ball undergoes simple harmonic motion (planar pendulum) over the same half-cycle, with the roles continually reversing. The repetition occurs because, for small amplitudes, a conical pendulum can be considered as the superposition of two planar pendulums of the same length and amplitude, but with a 90o phase difference. The uniform circular motion is actually not necessary. For small amplitudes, the general motion is elliptical, which is the superposition of two perpendicular simple harmonic motions of the same period but different amplitudes. The motion slowly degrades due to the fact that the collisions are not perfectly elastic. The weak inelasticity is demonstrated directly with repeated one-dimensional collisions, which show an accumulative effect where the balls eventually move together in contact. Finally, for large amplitudes, a dramatic breakdown of the repetition occurs due to nonlinearity. The period of the uniform circular motion decreases, whereas the period of the planar motion increases, so the collision second collision fails be head-on. This causes motion to not repeat and to be complicated (probably chaotic). Another reason for the high-amplitude behavior is that the motion is very sensitive to the lack of an initial collision that is precisely head-on. Supports the following NPS courses: PH3119 (Oscillation and Waves), PH3451 (Fundamental Acoustics), PH4454 (Sonar Transduction).