# An Analytical Approach to Eddy Current in Electromagnetic Damping

## TL;DR

This paper presents an analytical method to calculate eddy currents in a spinning gyroscope within a magnetic field, simplifying Maxwell's equations to a Poisson boundary value problem, and validates the model with experimental data.

## Contribution

It introduces a simplified analytical approach to determine eddy currents in gyroscopes, reducing complex Maxwell equations to a solvable Poisson boundary problem.

## Key findings

- Derived a closed-form expression for eddy currents
- Calculated rotation frequency over time with 8.61% error
- Validated the model against experimental data

## Abstract

An analytical method of calculating eddy current in a metallic spinning gyroscope in external magnetic field is presented. With reasonable assumptions, the problem is simplified from the time-dependent one governed by Maxwell equations to the boundary value problem of Poisson equation, which yields a closed form expression of the eddy current. The rotation frequency as a function of time is calculated, compared with experiment and the relative error is found to be 8.61%.