Jerk and Hyperjerk in a Rotating Frame of Reference

TL;DR

This paper explores the mathematical relations of jerk and hyperjerks between inertial and rotating frames, providing insights useful for physics education and understanding motion in non-inertial reference frames.

Contribution

It derives the relations for higher-order derivatives of motion in rotating frames, extending the understanding of kinematic quantities beyond acceleration.

Findings

Derived formulas relating jerk and hyperjerks in rotating and inertial frames

Provides educational insights into non-inertial reference frame kinematics

Enhances understanding of motion derivatives in physics teaching

Abstract

Jerk is the derivative of acceleration with respect to time and then it is the third order derivative of the position vector. Hyperjerks are the n-th order derivatives with n>3. This paper describes the relations, for jerks and hyperjerks, between the quantities measured in an inertial frame of reference and those observed in a rotating frame. These relations can be interesting for teaching purposes.