arXiv subjects

Al Cheremensky

Publications and source records attributed to Al Cheremensky.

3 recordsLinked to original sources

arXiv2017

Systems of Cosserat--Zhilin in Newtonian Mechanics

Mechanical systems of Cosserat--Zhilin are introduced as the main object of Newtonian (non--relativistic) mechanics on the base of new notions of vector calculus - sliders and screw measures (bi-measures). The differential equations of motion are derived for different types of Cosserat--Zhilin systems in the case where Stocks theorem is applicable. The paper defines multiplicative groups which represent the measure of stress as a (well-defined) linear isotropic map of {strain} tensor or tensor of {strain velocities} for classical and polar continua in 2- and 3-dimensional cases.

math-ph↗

arXiv2013

On Concept of Mechanical System

The paper gives a screw axiomatics of rational mechanics, namely: 1. introduces the main measures of mechanics: the mass measure, the scalar and (vector) screw measures of motion, the (vector) screw measure of impressed action, the increment velocity of the vector measure of motion, the (vector) screw measure of constraint action; 2. postulates the (stronger) local integral form of conservation law for the vector measuare of motion (fundamental principle of dynamics), and 3. defines the central concept of rational mechanics {mechanical system being realized in the form of all classical mechanical systems (mass-points, rigid bodies, continua, point-bodies, etc.). The presentation is based on new notions of vector calculus -- homogeneous and inhomogeneous vector and tensor slider-functions and screw measures.

math-ph↗

arXiv2011

On Foundations of Newtonian Mechanics

Being based on V. Konoplev's axiomatic approach to continuum mechanics, the paper broadens its frontiers in order to bring together continuum mechanics with classical mechanics in a new theory of mechanical systems. There are derived motion equations of `abstract' mechanical systems specified for mass-points, multibody systems and continua: Newton-Euler equations, Lagrange equations of II kind and Navier-Stokes ones. Quasi-linear constitutive equations are introduced in conformity with V. Konoplev's definition of stress and strain (rate) matrices.

math-ph↗