Related papers: On Concept of Mechanical System
We obtain estimates of all components of the velocity of a 3D rigid body moving in a viscous incompressible fluid without any symmetry restriction on the shape of the rigid body or the container. The estimates are in terms of suitable norms…
In this review we summarize theoretical progress in the field of active matter, placing it in the context of recent experiments. Our approach offers a unified framework for the mechanical and statistical properties of living matter:…
This treaties aims to introduce a speculative framework to comprehend modern metrology. In a classical sense, measurement measures physically existing quantities, such as length, mass, and time. By contrast, modern measurement measures a…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…
The development of scientometric indicators and methods for evaluative purposes, requires a multitude of assumptions, conventions, limitations, and caveats. Given this, we cannot permit ambiguities in the key concepts forming the basis of…
The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems dynamics is equivalent to the choice of the corresponding metric…
This paper presents a unified approach for inverse and direct dynamics of constrained multibody systems that can serve as a basis for analysis, simulation, and control. The main advantage of the formulation of the dynamic is that it does…
The three major theoretical principles of quantum mechanics relevant to its interpretation are: (T1), linearity; (T2), invariance under certain groups; and (T3) the orthogonality and isolation of the different branches of the state vector.…
Supmech, an algebraic scheme of mechanics integrating noncommutative symplectic geometry and noncommutative probability, subsumes quantum and classical mechanics and permits consistent treatment of interaction of quantum and classical…
This survey is dedicated to a new direction in the theory of dynamical systems: the dynamics of metrics in measure spaces and new (catalytic) invariants of transformations with invariant measure. A space equipped with a measure and a metric…
This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space'' and its rational powers. Positive spaces are 1-dimensional ``semi-vector…
In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools…
The equations of motion of a mechanical system subjected to nonholonomic linear constraints can be formulated in terms of a linear almost Poisson structure in a vector bundle. We study the existence of invariant measures for the system in…
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
We show how a metric space induces a linear functional (a "mean") on real-valued functions with domains in that metric space. This immediately induces a "relative" measure on a collection of subsets of the underlying set.
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
In Willems' behavioral systems theory, a dynamical system is identified with the set of all trajectories compatible with its laws of motion. In the linear time-invariant setting this trajectory set is a linear subspace, and its algebraic…