On the Possibility of the Jerk Derivative in Electrical Circuits

Abstract

A subclass of dynamical systems with a time rate of change of acceleration are called Newtonian jerky dynamics. Some mechanical and acoustic systems can be interpreted as jerky dynamics. In this paper we show that the jerk dynamics are naturally obtained for electrical circuits using the fractional calculus approach with order γ. We consider fractional LC and RL electrical circuits with 1⩽γ<2 for different source terms. The LC circuit has a frequency ω dependent on the order of the fractional differential equation γ, since it is defined as ω(γ)=ω0γγ1-γ, where ω0 is the fundamental frequency. For γ=3/2, the system is described by a third-order differential equation with frequency ω~ω03/2, and assuming γ=2 the dynamics are described by a fourth differential equation for jerk dynamics with frequency ω~ω02.