About integrated invariance, arising at resonance of oscillations in some types non-conservative mechanical systems

TL;DR

This paper derives an integrated invariant of movement for certain non-conservative mechanical systems exhibiting one-frequency periodic oscillations, enhancing understanding of their dynamic behavior.

Contribution

It introduces a new integrated invariant for non-conservative holonomic systems with periodic oscillations, expanding the theoretical framework of such systems.

Findings

Derived an invariant for systems with one-frequency oscillations

Applicable to autonomous non-conservative holonomic systems

Provides insights into the dynamics of oscillatory systems

Abstract

For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of movement.