Two-Body Motion in Central Conservative Force Fields

TL;DR

This paper compares two-body motion under gravitational and elastic forces, analyzing their trajectories and force dependencies to understand their dynamic behaviors and differences.

Contribution

It provides a comparative analysis of two-body motions in gravitational and elastic force fields, highlighting their trajectory characteristics and force dependencies.

Findings

Gravitational force leads to closed trajectories.

Elastic force results in open trajectories.

Force dependencies are inverse and direct square displacements.

Abstract

The two-body motion for the gravitational and linear elastic central conservative force field is discussed by comparing the differential equations of motions. The inverse and direct square displacement dependency of the two force types is shown as emerging in the trajectories. The closed (for the gravitational field) and open (for the particular dumbbell elastic system considered) character of the trajectory is discussed.