Simple nonlinear jerk functions with periodic solutions

Abstract

The appearances of jerk, the third time derivative of displacement, in several papers of mathematical and physical content are reviewed. Two simple nonlinear jerk functions, all of whose solutions are periodic, are introduced and solved. The first has period dependent on initial acceleration but independent of amplitude, and is related to the second-order cubic oscillator. The second, with intrinsically third-order dynamics, has period dependent also on initial displacement. A possible bearing on chaotic jerk functions is mooted.