D'Alembert-Lagrange principle for point masses yields a system of weighted balancing unit vectors in the three dimensional Euclidean Space

TL;DR

This paper demonstrates that applying the D'Alembert-Lagrange principle to point masses results in a weighted balancing condition of unit vectors in three-dimensional Euclidean space, providing a geometric interpretation of the principle.

Contribution

It introduces a novel geometric perspective by linking the D'Alembert-Lagrange principle to weighted balancing of unit vectors in 3D space.

Findings

Weighted balancing condition of unit vectors derived from the principle

Geometric interpretation of D'Alembert-Lagrange principle in 3D

Connection between mechanical construction and vector balancing

Abstract

In this paper, we prove that D'Alembert-Lagrange principle for point masses using Lagrange-Mach's mechanical construction yields a weighted balancing condition of unit vectors in $\mathbb{E}^{3}.$