Persistent Passive Hopping and Juggling is Possible Even With Plastic Collisions

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and oneball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a lower point-mass hand is connected by a spring to the ground and an upper point-mass ball is caught with an inelastic collision and then re-thrown into gravitational free flight. The two systems have identical dynamics. Despite inelastic collisions between non-zero masses, these systems have special symmetric energy-conserving periodic motions where the collision is at zero relative velocity. Additionally, these special periodic motions have a non-zero sized, one-sided region of attraction on the higher-energy side. For either very large or very small mass ratios, the one-sided region of attrac...

• Type: Journal
• Year: 2002
• Where: IJRR
• Authors: Anindya Chatterjee, R. Pratap, C. K. Reddy, Andy Ruina
• Keywords: Collisions, IJRR 2002, Inelastic Collisions, Periodic Motions