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.

An efficient approach to solving fractional Van der Pol–Duffing jerk oscillator

“…It is noted that as e  0 into (54) and (55) the results reduce to those obtained before in (31) and (32).…”

“…A jerk equation has vast applications in physics and daily life. It has been set to have numerous applications in various areas of science, such as laser physics electrical circuits, acoustics, dynamical processes, and mechanics [28][29][30][31][32]. Jerk is also organized to be governed the flow of a thin-film viscous fluid with a free surface where the surface tension effects play a role typically leading to a third-order equation governing the form of the free surface of the fluid.…”

Formal expansion method for solving an electrical circuit model

“…This is consistent with the theory that as it is the second order formal expansion solution, the order of accuracy is 2 in the time-scale 1. As final remarks, knowing the accuracy of the formal expansion method, we could extend the application of this method to solve other mathematical engineering problems, such as those studied by researchers in [16][17][18][19][20][21][22][23][24][25][26]. Possible other problems to be solved using the formal expansion method could be those in [27][28][29][30][31][32][33][34][35][36][37].…”

An innovative technique to solve a fractal damping Duffing-jerk oscillator

“…Many different phenomena in physics and the engineering sciences are represented by nonlinear systems of differential equations, which include the third-order derivative. The importance of these phenomena appears greatly in many applications in daily life, for example, in electrical circuits, mechanics, dynamic processes, and acoustics [1][2][3][4][5][6]. The study of this type of system has gained importance since Schot defined the rate of change of the acceleration vector as the jerk (1978) [7].…”