A two-body problem of classical electrodynamics: the one-dimensional case

Estimation of Time- and State-Dependent Delays and Other Parameters in Functional Differential Equations

“…Since W gives the value of the lagged time, we can interpret this ,condition as follows: Whenever one event precedes another ( w(t l ) < w(t 2 ) ), then the effect of the first event must be felt by the state before the effect of the second event ·(since the monotonicity of w implies tl < t 2 ). In both the models of [7] and [10], (when there is enough smoothness in the problem so that the delay is differentiable) this condition is satisfied.…”

“…A problem from electrodynamics involving state-dependent delays was considered by Driver (e.g., [7] and [8]). In [8J he derives and analyzes systems of equations of the general form: }ri(t) = fi(t, yet), y(g2(t, yet»~), ... , y(gm(t, yet»~»~ (i-I, ... ,n).…”

“…Such equations can be used (as in [7], for example) to describe the motion of two electrically charged particles.…”

An analysis on the stability of a state dependent delay differential equation

“…Driver [5,6] and Driver and Norris [7] developed a fundamental theory and proved local existence and uniqueness theorem for SDDE having Lipschitz continuous initial functions. Winston [8] showed that SDDE has a unique solution under some conditions in addition to continuos initial function.…”

State-dependent distributed-delay model of orthogonal cutting

“…Examples include wheel-shimmy [37,41], delaycoupled networks [40], predictive control systems [30,16,31] and machine tool vibrations [36,11,27,32]. Differential equations involving state-dependent delays also often show up in different fields of science, such as classical electrodynamics [13], population models [26,35], market dynamics [6], and, again, machine tool vibrations [23,15,3,28,29]. In this paper, a model is presented for machining, which involves a combination of these two types of delays: a state-dependent distributed delay.…”