Two-dimensional array for operating an oscillator in Euclidean space $\mathbb{R}^3$, as a power multiplier

TL;DR

This paper models a coupled oscillator system involving a seesaw and pendulum on a slope, using a transformation matrix to analyze energy variations and system symmetry in Euclidean space.

Contribution

It introduces a matrix-based approach to describe the dynamics of a complex oscillator system in Euclidean space, highlighting energy transfer and symmetry preservation.

Findings

The system's behavior can be effectively represented by a transformation matrix.

Energy loss and system response are visualized through matrix variations.

The approach aids in understanding energy exchange in coupled oscillators.

Abstract

In the present study an oscillator system formed by a seesaw connected to a simple pendulum coupled to a mobile platform with a certain slope, is analyzed. The observed properties of the system when faced with a possible displacement of the mobile are affected in terms of energy loss, which can be reflected in the angle, the variation of apparent weight and the height. The possible variations which can be introduced modify these parameters, so that the system tries to compensate them in order to preserve its symmetry. The working of this system can be described by means of a transformation matrix where the nature of the movement is represented. Such tool enables us to observe the variations that the system may experience as rotation and translation functions. Therefore, the matrix offers a clear visualization of the values expressed and thus of the need to either provide or extract energy to or from the system.