Follow up question. Is this in the neighborhood of what you’re saying?
constant tau (τ)
usually denoted by the Greek letter τ (tau), is the parameter characterizing the speed of response to a step input of a first-order, linear time-invariant (LTI) system.
2pi=phi 1.61803… ratio between the radius and the circumference
LIMIT OF IMPULSE RESPONSE or TOTAL IMPULSE (of collision) … or force of impact?
pi 3.14159… ratio between the diameter and the circumference
The Dirac delta is used to model a tall narrow spike function (an impulse), and other similar abstractions such as a point charge or point mass.[6][7] For example, to calculate the dynamics of a billiard ball being struck, one can approximate the force of the impact by a Dirac delta. In doing so, one can simplify the equations and calculate the motion of the ball by only considering the total impulse of the collision, without a detailed model of all of the elastic energy transfer at subatomic levels (for instance).
red: force of impact
blue: (impulse impact/response)
yellow: motion (extension of interaction)
the impact can be what we consider a crash… or it can be… very small… just a presence