Related papers: On Concept of Mechanical System
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. The physical interpretation of the notion of relative acceleration is discussed. The notions of deformation acceleration, shear…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…
We discuss a role of a momentum vector in the description of dynamics of systems with variable mass, and show some ambiguity in expressing the 2nd Newtonian law of dynamics in terms of momentum change in time for variable-mass systems. A…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
We present a framework to take new measurements in nematic systems that contain active elements such as molecular motors. Spatio-temporal fields of stress, traction, velocity, pressure, and forces are estimated jointly from microscopy…
This novel approach to the foundation of the physical theory begins with Hermann von Helmholtz fundamental analysis of basic measurements. We explain the mathematical formalism from the operationalization of basic observables. According to…
Discrete mechanics proposes an alternative formulation of the equations of mechanics where the Navier-Stokes and Navier-Lam\'e equations become approximations of the equation of discrete motion. It unifies the fields of fluid and solid…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
The paper presents a new study method of mechanic vibrations with the help of the data acquisition systems. The study of vibrations with the help of data acquisition systems allows the solving of some engineering problems connected to the…
The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…
Motion capture systems, used across various domains, make body representations concrete through technical processes. We argue that the measurement of bodies and the validation of measurements for motion capture systems can be understood as…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
A brief summary of the objections to the relational nature of inertial mass, gravitational mass and electric charge is presented. The objections are refuted by showing that the measurement process of comparing an instrument reference clock…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is…