相关论文: Modeling and experimentation with asymmetric rigid…
The problem of a cylinder of mass m and radius r, with its center of mass out of the cylinder axis, rolling on an incline that makes an angle with respect to the horizontal is analyzed. The equation of motion is partially solved to obtain…
We present an experimental study of the motion of a circular disk spun onto a table. With the help of a high speed video system, the temporal evolutions of (i) the inclination angle $\alpha$, (ii) the angular velocity $\omega$ and (iii) the…
The motion of a rigid, spinning disk on a flat surface ends with a dissipation-induced finite-time singularity. The problem of finding the dominant energy absorption mechanism during the last phase of the motion generated a lively debate…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
This note adds some critical remarks on the discussion presented in the McDonald's paper ([1]) on stability of steady motion of the well known problem of a disk rolling on a rough horizontal plane.
The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we…
We designed a very simple asymmetric rolling spool and we studied it experimentally, in the librational regime, by using a video camera and video analysis software. Comparison of experimental results and theoretical analysis allows…
We study the deflection by gravity of a circular elastic disk deposited on a rigid support. The axisymmetric deflection induces a compressive orthoradial stresses which leads to a wrinkling instability above a critical threshold of the…
The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks. The following experiment serves to clearly demonstrate the transition…
A theory is developed for the dynamics of eccentric perturbations $[\propto \exp(\pm i\phi)]$ of a disk galaxy residing in a spherical dark matter halo and including a spherical bulge component. The disk is represented as a large number $N$…
A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using Molecular Dynamics Simulations, and…
In this chapter, we review some of the interesting consequences that tilt between the spin axis of the black hole and angular momentum axis of the accretion disk can have on the dynamics, thermodynamics, and observational appearance of…
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…
A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Slim accretion disks idea emerged over 30 years ago as an answer to several unsolved problems. Since that time there was a tremendous increase in the amount of observational data where this model applies. However, many critical issues on…
Axisymmetric accretion disks in vicinity of a central compact body are studied. For the simple models such as vertically isothermal disks as well as adiabatic ones the exact solutions to the steady-state MHD (magneto-hydrodynamic) system…
The problem of a rigid disk rolling down a ramp is a classic problem given to students in introductory mechanics courses. In contrast, systematic studies on the rolling behavior of an ellipse have only recently emerged. Unlike a rolling…
Spinning ice discs in nature have been reported for more than a century, yet laboratory experiments have yielded diverse observations and contradictory explanations, leaving the mechanism behind the disc motion elusive. Here we combine…