相关论文: On Foundations of Newtonian Mechanics

Despite its apparent simplicity, Newtonian Mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtleties concern fundamental issues such as, e.g., the number of independent laws needed…

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…

The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A…

A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…

In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions; momentum, angular momentum, center of mass, force and torque are defined for $N$…

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…

This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…

The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…

The basic equations describing a Newtonian universe with uniform pressure are reexamined. We argue that in the semi-classical formulation adopted in the literature the continuity equation has a misleading pressure gradient term. When this…

The paper gives an introduction to rate equations in nonlinear continuum mechanics which should obey specific transformation rules. Emphasis is placed on the geometrical nature of the operations involved in order to clarify the different…

I discuss the physical basis of classical mechanics, such as expressed commonly using the framework of Newton's Principia. Newton's formulation of the laws of motion is seen to have quite a few ambiguities and shortcomings. Therefore I…

We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…

We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in…

The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion…

In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems.…

One of the founders of the mechanics of nonoholonomic systems is Voronec who published in 1901 a significant generalization of the Caplygin's equations, by removing some restrictive assumptions. In the frame of nonholonomic systems, the…

This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…

We propose a new point of view for interpreting Newton's and Einstein's theories of gravity. By taking inspiration from Continuum Mechanics and its treatment of anisotropies, we formulate new gravitational actions for modified theories of…

Classical field theories together with the Lagrangian and Eulerian approaches to continuum mechanics are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, space…

The Euler and Navier-Stokes fluid mechanics equations are derived using a modified statistical mechanical approach using theory taken from the Chapman-Enskog perturbation analysis used to support the lattice Boltzmann method. Additional…