Thinking towards Motion Modeling: on High-order Derivatives of Displacement

TL;DR

This paper explores advanced motion modeling in physics by using time-variant autocorrelation polynomials to mathematically describe higher-order derivatives of displacement, such as jerk and snap.

Contribution

It introduces a novel approach to understanding physical motion through high-order derivatives using autocorrelation polynomials, extending beyond traditional velocity and acceleration.

Findings

Mathematical framework for higher-order derivatives of motion

Potential explanation for physical concepts like jerk and snap

New insights into motion modeling in physics

Abstract

This note is concerned with the problem of motion modeling in Physics. We aim to use the Time-Variant Local Autocorrelation Polynomial to understand the mathematical model of motion description. The mathematical explanation of the existence of physical concepts, beyond Velocity and Acceleration, like Jerk, Snap, Crackle, and Pop could be revealed.