Some remarks on the periodic motions of a bouncing ball
Abstract
We consider the vertical motion of a free falling ball bouncing elastically on a racket moving in the vertical direction according to a regular 1-periodic function f. For fixed coprime p,q we study existence, stability in the sense of Lyapunov and multiplicity of p periodic motions making q bounces in a period. If f is real analytic we prove that one periodic motion is unstable and give some information on the set of these motions.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.