相关论文: A Problem of Relative, Constrained Motion
Problems involving rotating systems analyzed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. One of the problems that I…
We discuss the theoretical solution to the differential equations governing accelerating edge dislocations in anisotropic crystals. This is an important prerequisite to understanding high speed dislocation motion, including an open question…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is…
In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the…
We analyze the motion of a particle in the gravity field along a family of differentiable curves taking into account the Coulomb friction forces. A parametric equation of the optimal curves is given that generalizes the cycloid one in this…
We study the motion of smooth, closed, strictly convex hypersurfaces in Rn+1 expanding in the direction of their normal vector field with speed depending on the k-th elementary symmetric polynomial of the principal radii of curvature. As an…
We show how the motion of free material test particles in arbitrary spatial flows is easily determined within the context of ordinary vector calculus. This may be useful for everyone, including engineers and other non-specialists, when…
An interesting phenomenon that occurs in projectile motion, the "coming and going", is analyzed considering linear air resistance force. By performing both approximate and numerical analysis, it is showed how a determined critical angle and…
(abbreviated) In this note we consider, in a weak-field limit, a relativistic linear motion of two particles with opposite signs of masses having a small difference between their absolute values $m_{1,2}=\pm (\mu\pm \Delta \mu) $, $\mu >…
We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the Special Theory of Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in…
We study slowly moving solutions of the real Ginzburg-Landau equation on the line, by a method due to J. Carr and R.L. Pego. These are functions taking alternately positive or negative values on large intervals. A consequence of our…
We present a numerical method for the solution of Newton's problem of least resistance in the class of convex functions using a convex hull approach. We observe that the numerically computed solutions possess some symmetry. Further, their…
An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…
I discuss the influence of adding the air resistance and the kinetic friction to the classical mechanics homework-problem: finding the motion of a body sliding down a hemispherical hill. For a physically realistic ($\propto v^2$) form of…
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations…
We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced in number in two cases:…
The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is…