# Features of description of composite system's motion in twist-deformed space-time

## TL;DR

This paper investigates how twist-deformed space-time affects the motion of composite systems, revealing that deformation influences the center-of-mass motion differently than individual particles and depends on system composition.

## Contribution

It demonstrates that with inverse mass proportionality in noncommutativity parameters, the center-of-mass motion becomes independent of relative motion, preserving the weak equivalence principle.

## Key findings

- Center-of-mass motion depends on relative motion in twist-deformed space
- Inverse proportionality of noncommutativity parameters to mass is crucial
- Coordinate relations become independent of system composition under certain conditions

## Abstract

Composite system made of $N$ particles is considered in twist-deformed space-time. It is shown that in the space the motion of the center-of-mass of the system depends on the relative motion. Influence of deformation on the motion of the center-of-mass of composite system is less than on the motion of individual particles and depends on the system's composition. We conclude that if we consider commutation relations for coordinates of a particle to be proportional inversely to its mass, the commutation relations for coordinates of composite system do not depend on its composition and are proportional inversely to system's total mass, besides the motion of the center-of-mass is independent of the relative motion. In addition we find that inverse proportionality of parameters of noncommutativity to mass is important for considering coordinates in twist-deformed space as kinematic variables and for preserving of the weak equivalence principle.