The $r$-equilibrium Problem

TL;DR

This paper introduces the $r$-equilibrium problem, exploring its mathematical connections and physical interpretations for different values of r, including applications to Newton's third law and torque equilibrium.

Contribution

It defines the $r$-equilibrium problem and links it to the map $det^{S^r}$, providing new insights into equilibrium conditions for various r values.

Findings

Connection between $r$-equilibrium and $det^{S^r}$ map

Application of $r=2$ case to Newton's third law

Analysis of $r=3$ case related to torque equilibrium

Abstract

In this paper we introduce the $r$-equilibrium problem and discuss connections to the map $det^{S^r}$. The case $r=2$ is an application of Newton's third law of motion, while $r=3$ deals with equilibrium of torque-like forces.