Apollo's Voyage: A New Take on Dynamics in Rotating Frames

TL;DR

This paper clarifies the complex nature of pseudoforces in rotating and accelerating frames, revealing additional components beyond traditional explanations, and demonstrates their application through a simple example.

Contribution

It introduces a comprehensive understanding of pseudoforces in general accelerating frames, highlighting a new component arising from combined translation and rotation effects.

Findings

Identification of a new pseudoforce component in accelerating frames

Demonstration of the application of these dynamics in a simple example

Clarification of common misconceptions about pseudoforces

Abstract

We first demonstrate how our general intuition of pseudoforces has to navigate around several pitfalls in rotating frames. And then, we proceed to develop an intuitive understanding of the different components of the pseudoforces in most general accelerating (rotating and translating) frames: we show that it is not just a sum of the contributions coming from translation and rotation separately, but there is yet another component that is a more complicated combination of the two. Finally, we demonstrate using a simple example, how these dynamical equations can be used in such frames.