2013/02/28 by Al Cheremensky, Cheremensky, Al
Computer Science · Mathematics · #68T40 #70B10 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1302.7092
openalex publication_date 2013/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.