Study of the Phase-Lock Phenomenon for a Circular Slingatron

摘要

The phase-lock phenomenon of a mass sled sliding along in a circular slingatron is studied both numerically and analytically. Parameters that describe a slingatron, in which the phase angle of the swing arms increases quadratically in time, are found to be simply related to the sled's speed during phase lock. The time required for phase lock to occur is related to a simple exponential function of the gyration speed and the coefficient of friction between the sled and track. Accurate time histories describing the motion of the accelerating sled are expressed in terms of confluent hypergeometric functions 1F1. These results are then used to obtain physical insight into why the phase- lock phenomenon takes place and to describe the important role that friction plays by damping the oscillatory motion of the sled.