Continuous and Symmetrical Transformations in the Framework of Classical Particle Systems

Abstract

Historically, symmetry has been associated with beauty and perfection, something that is merely a visual characteristic. However, in the realm of physics, symmetry is fundamental: it exists in physical systems and even in the laws of physics. In this study, only one particular type of symmetrythe continuous symmetry-is discussed in great depth. While a discussion of why symmetry exists is not the concern of this paper, the connection that exists between continuous symmetries and conservation laws, through Noether's theorem, is the focus of this study. Despite many articles and books that seek to understand Noether's theorem using Group Theory and Lie symmetry, this study explores the Noether's theorem (and Noether's inverse theorem) for nonrelativistic classical systems using ordinary calculus and an understanding of the concept of continuous transformations.