Influence of the Conservation Angular Momentum Law and the mathematical models for Continuum Mechanics and Kinetics

Author(s)

Abstract
The most common systems are open non-equilibrium non-stationary systems. From the previously formulated equations and some experiments, the connection between the gradients of physical quantities and the moment of momentum (force) is traced. The main equations of the theory are the Liouville equation, constructed on the basis of Hamilton's theory for closed systems, and the equations constructed using it. The article investigates some processes from this trace. The use of the Hamiltonian formalism and the dependence of the force only on the distance between particles limit the study. In the collision integral, for example, for a rarefied gas, the Lennard-Jones potential is often used, which is not of the type considered. The foregoing forces us to turn to the study of the influence of forces of a more general form on the equations of mechanics. Hamilton’s formalism traces the behavior of closed systems. The general form of boundary conditions and forces changes the theory proposed in the works by N.N. Bogolyubov. The results of the reformulation are discussed. Even in classical theory, after taking moments, we arrive at Boltzmann’s theory at no symmetric stress tensor. The symmetric tensor is obtained after the assumption of a small effect of no symmetry and from the condition of the balance of forces. The requirement of simultaneous fulfillment of the laws of conservation of forces and moments of forces leads to the existence of two solutions. To take into account the angular momentum, in addition to the conditions for the equilibrium of forces, the law of equilibrium of the moments of forces is required in the calculations. From it, the degree of no symmetry of the stress tensor is determined. In previous works the contribution of the distributed moment of force illustrate to the problems of continuum mechanics and the kinetic theory. Examples of the solution to the problem of fluid mechanics, the theory of elasticity and kinetic theory were given early. Here we discuss the theory needed to account for the lack of symmetry of the stress tensor.

Keywords
equations and boundary conditions, kinetic theory., the influence of the angular momentum, dislocation, vacancies.

Cite this paper
Evelina Prozorova, Influence of the Conservation Angular Momentum Law and the mathematical models for Continuum Mechanics and Kinetics , SCIREA Journal of Physics. Volume 10, Issue 1, February 2025 | PP. 1-15. 10.54647/physics140652

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