The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag...The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag is investigated for discrete environment. The analysis of the recording of the Lagrangian function for the collective interaction of the particles with the change of the center of inertia of the moving particles and the effect influence of the angular momentum were used. The equations for gas are calculated from the modified Boltzmann equation and the phenomenological theory. For a rigid body the equations were used of the phenomenological theory, but their interpretation was changed. The nonsymmetric stress tensor was obtained. The Boltzmann equation is written with an additional summand. This situation is typical for discrete environment as the transition from discrete to continuous environment is a key to the issue of mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The Hilbert paradox was being solved. The simplest problem of the boundary layer continuum (the Falkner-Skan task) and the kinetic theory are discussed. A draw attention at the delay process would be suggested for the description of discrete environment. Results are received for some special cases.展开更多
The most common systems are open 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...The most common systems are open 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 article investigates 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 moment, 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. The work illustrates the contribution of the distributed moment of force 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 are given. A correspondence is established between the terms of the Liouville equation with more general and traditional forces. Previously, the influence of moments in boundary layer problems, jet problems, and the simplest problems of elasticity theory was considered. The work proves the important role of distributed moments in the formation of new structures.展开更多
文摘The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag is investigated for discrete environment. The analysis of the recording of the Lagrangian function for the collective interaction of the particles with the change of the center of inertia of the moving particles and the effect influence of the angular momentum were used. The equations for gas are calculated from the modified Boltzmann equation and the phenomenological theory. For a rigid body the equations were used of the phenomenological theory, but their interpretation was changed. The nonsymmetric stress tensor was obtained. The Boltzmann equation is written with an additional summand. This situation is typical for discrete environment as the transition from discrete to continuous environment is a key to the issue of mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The Hilbert paradox was being solved. The simplest problem of the boundary layer continuum (the Falkner-Skan task) and the kinetic theory are discussed. A draw attention at the delay process would be suggested for the description of discrete environment. Results are received for some special cases.
文摘The most common systems are open 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 article investigates 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 moment, 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. The work illustrates the contribution of the distributed moment of force 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 are given. A correspondence is established between the terms of the Liouville equation with more general and traditional forces. Previously, the influence of moments in boundary layer problems, jet problems, and the simplest problems of elasticity theory was considered. The work proves the important role of distributed moments in the formation of new structures.
