Class

Article

College

College of Science

Department

English Department

Faculty Mentor

Boyd Edwards

Presentation Type

Poster Presentation

Abstract

We developed a 4th order Runge-Kutta program for the problem of two uniformly magnetized spheres, one sphere orbiting a second stationary sphere, by means of their magnetic fields. There are four coupled ordinary differential equations that describe the motion of the orbiting magnet. We graphed the solutions to these equations for a range of initial conditions and determined the chaotic indicator called the Lyapunov exponent (LE) in each case. A graph of the potential energy was also made. We look at the numerical values and graphs of the four equations and see how much they differ for a range of initial conditions to determine if the system is periodic or chaotic for given initial conditions.

Location

Logan, UT

Start Date

4-7-2022 12:00 AM

Included in

Physics Commons

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Apr 7th, 12:00 AM

Simulation of the Nonlinear Dynamics of a Spherical Magnet in the Field of a Second Stationary Magnet

Logan, UT

We developed a 4th order Runge-Kutta program for the problem of two uniformly magnetized spheres, one sphere orbiting a second stationary sphere, by means of their magnetic fields. There are four coupled ordinary differential equations that describe the motion of the orbiting magnet. We graphed the solutions to these equations for a range of initial conditions and determined the chaotic indicator called the Lyapunov exponent (LE) in each case. A graph of the potential energy was also made. We look at the numerical values and graphs of the four equations and see how much they differ for a range of initial conditions to determine if the system is periodic or chaotic for given initial conditions.