Noetherian symmetries of noncentral forces with drag term

TL;DR

This paper investigates the Noetherian symmetries of second-order differential equations with noncentral forces, including drag, revealing how symmetries relate to integrals in equations like Emden-Fowler.

Contribution

It identifies the symmetries of noncentral force equations with drag, linking them to known integrals and extending symmetry analysis to more complex force fields.

Findings

Symmetries correspond to integrals derived from Emden-Fowler equation.

Both position and velocity dependent forces analyzed.

Results extend symmetry methods to nonconservative systems with drag.

Abstract

We consider the Noetherian symmetries of second-order ODEs subjected to forces with nonzero curl. Both position and velocity dependent forces are considered. In the former case the first integrals are shown to follow from the symmetries of the celebrated Emden-Fowler equation.