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Proceedings Paper

Influence of dispersion in mechanics
Author(s): E. V. Prozorova
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Paper Abstract

One can exploit different approaches to describe gas, liquid or solid state. It is possible to consider medium as population of separate molecules, the motion of each molecule being investigated by Newton's or quantum laws. More rough description can be applied through the distribution function of the molecules, but the simplest way is to write the conservation laws in continuous mechanics. In classical mechanics these are the laws for mass, linear momentum, energy, but the law of angular momentum is also fundamental. For particles without structure this law is not formulated. For particles with structure this law is formulated as a local law. The conservation laws are found experimentally and expressed in an integral form. It is possible to pass from the integral form to differential form for smooth functions. This assumes the possibility to pinch a volume to a point. Often the conservation laws are received as balance relations for an elementary volume put in infinity space. Every law deals with its own elementary volume. However, the angular momentum conservation law assumes the exsitence of a coordinate system and radius vector from the origin to an elementary volume. So the symmetry of the angular momentum law is postulated in spite of the fact that in general case the movement of mass points is noninertial. Large gradients lead to large remainder terms when we turn from an integral form to a differential one. One of the aims of our analysis is to define relation between the conservation laws in continuum mechanics and the variation of the angular momentum in an elementary volume. Passage from the description of motion of a system of mass points to the motion of the elementary volume as a whole is insufficiently studied in mechanics. This question is advanced mostly for a rarefied gas by Bogolubove N.N., his pupils and co-workers who use N-partial distribution function to describe motion of a system of N mass points. It was done to receive an equation for one-partial distribution function in kinetics. It is essentially that Hamiltonian formalism must be exploited for deduction the equation for N-partial distribution function. The latter supposition provides transition from the Liouville equation to the kinetic equation for the mass points at known additional conditions. However the Hamiltonian formalism can be used in the case of mechanics without dissipation. For large gradients and perturbing surfaces the formalism is absent.

Paper Details

Date Published: 5 April 2004
PDF: 8 pages
Proc. SPIE 5400, Seventh International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering, (5 April 2004); doi: 10.1117/12.555471
Show Author Affiliations
E. V. Prozorova, St. Petersburg State Univ. (Russia)


Published in SPIE Proceedings Vol. 5400:
Seventh International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering
Alexander I. Melker, Editor(s)

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