Related papers: On Concept of Mechanical System
We address the problem of attitude stabilization of a rigid body, in which neither the angular velocity nor the instantaneous measurements of the attitude are used in the feedback, only body vector measurements are needed. The design of the…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of…
Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with…
Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…
We consider the (complete) Euler system describing the motion of a compressible perfect fluid. We propose a platform suitable for constructing the statistical solutions. The main ingredients of our approach include: 1. The concept of…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
The first part of the article is, in fact, the classical Routh method delivered in the language of contemporary theory of Lagrangian systems. But the Routh method deals only with concrete equations and, therefore, can be applied only in the…
The paper proposes a technique to estimate the angular velocity of a rigid body from vector measurements. Compared to the approaches presented in the literature, it does not use attitude information nor rate gyros as inputs. Instead, vector…
It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical…
Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
We numerically study a simple sliding system: a rigid mass pulled by a spring with a strong in-plane stiffness anisotropy and a small misalignment angle. Simulations show that the apparent stick phase appearing in this system is in reality…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…