Year: 2025
Type: article
Abstract: We present a pairwise force law in a system of N particles that produces analytic solutions for an arbitrary number of particles, masses, and initial conditions. Each pair of particles interacts via a force that is proportional to the product of their masses and their separation distance, with the force directed radially. We show that, despite the N-body interaction, each particle behaves as if it interacts only with the center of mass of the system. This effective one-body interaction behaves as Hooke's law with a common frequency for all particles, with the familiar analytic solutions for the trajectories. With these analytic solutions, it is possible to efficiently simulate a collection of these particles and incorporate other external forces. As an example, we simulate the particles within an adiabatically expanding container and calculate pressure and temperature in both the attractive and repulsive cases.
Source: American Journal of Physics
DOI: 10.1119/5.0226894
Authors: Joseph West, Sean P. Bartz
Institution: Indiana State University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: Strong, Nuclear Physics
OpenAlex ID: W4409653642