How to construct of mechanics of the structured particles

TL;DR

This paper develops a comprehensive framework for the mechanics of structured particles, deriving their equations of motion, analyzing their unique properties, and connecting these mechanics to thermodynamics and statistical physics.

Contribution

It introduces a detailed derivation of the mechanics of structured particles, including Lagrange, Hamilton, and Liouville equations, and explains their relation to dissipative forces and entropy.

Findings

Derivation of equations of motion for structured particles

Explanation of how internal and spatial symmetries influence dynamics

Connection between structured particle mechanics and thermodynamics

Abstract

The mechanics of structured particles (SP) consisting from potentially interacting material points are discussed. For this purpose the derivation of the SP equation motion in the field of external forces is submitted. The differences between the properties of the dynamics of material point and properties of the dynamics of SP are analyzed. The explanation of how mechanics of the $SP$ leads to the account of dissipative forces is submitted. The derivation of Lagrange, Hamilton and Liouville equations for $SP$ Is shown. The question of why the motions of the SP are determined by the two types of symmetry: internal symmetry of the system and symmetry of space and how it leads to two types of energy and forces accordingly are discussed. It is shown how the concept of entropy arises in classical mechanics. The question how the mechanics of the SP leads to thermodynamics, statistical physics and kinetics is explained.