Centre of mass in spaces with torsion free flat linear connection

TL;DR

This paper investigates the concept of the center of mass within spaces that have a torsion-free flat linear connection, establishing conditions for its almost unique definition and describing the associated arbitrariness.

Contribution

It provides a detailed analysis of the center of mass in torsion-free flat spaces, clarifying its uniqueness and the nature of its arbitrariness.

Findings

Center of mass is almost uniquely defined under general conditions.

Explicit description of the arbitrariness in the definition.

Conditions for the existence and uniqueness of the center of mass.

Abstract

The concept "centre of mass" is analyzed in spaces with torsion free flat linear connection. It is shown that under sufficiently general conditions it is almost uniquely defined, the corresponding arbitrariness in its definition being explicitly described.