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The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a…
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:…
A two-dimensional \underline{Frenkel-Kontorova model} under a steady external force is used to study the nonlinear sliding friction between flat macroscopic surfaces with a lubricant layer in between. The nonequilibrium properties of the…
In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric…
The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a…
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…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
A bicycle wheel that was initially spinning freely was placed in contact with a rough surface and a digital film was made of its motion. Using Tracker software for video analysis, we obtained the velocity vectors for several points on the…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
We consider the motion of a particle in a two-dimensional spatially homogeneous mixing potential and show that its momentum converges to the Brownian motion on a circle. This complements the limit theorem of Kesten and Papanicolaou…
The dynamics of a tracer particle in a glassy matrix of obstacles displays slow complex transport as the free volume approaches a critical value and the void space falls apart. We investigate the emerging subdiffusive motion of the test…
We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on…
We investigate the sliding of objects on an inclined granular surface close to the avalanche threshold. Our experiments show that the stability is driven by the surface deformations. Heavy objects generate footprint-like deformations which…
We study a possibility of existence of localized two-dimensional structures, both smooth and non-smooth, that can move without significant change of their shape in a leading stream of compressible barotropic fluid on a rotating plane.
We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.
We introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. We investigate dynamical aspects of the system such as existence of first integrals,…
We study the two-dimensional motion of a self-propelling asymmetric bent rod. By employing slender body theory and the Lorentz reciprocal theorem, we determine particle trajectories for different geometric configurations and arbitrary…
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…
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…