Related papers: Cycloidal Paths in Physics
We study the motion of colloidal particles driven by a constant force over a periodic optical potential energy landscape. Firstly, the average particle velocity is found as a function of the driving velocity and the wavelength of the…
There are many examples of driven and active matter systems containing particles that exhibit circular motion with different chiralities, such as swimming bacteria near surfaces or certain types of self-driven colloidal particles. Circular…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we…
The Rattleback is a very popular science toy shown to students all over the world to demonstrate the non-triviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the…
The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…
In the first part of the article using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ($\mu$). A parametric equation for the trajectory of…
A spatial surface is a compact surface embedded in the $3$-sphere. We assume that a spatial surface is oriented and that each connected component of a spatial surface is neither a disk nor without a boundary. A diagram of a spatial surface…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices. The problems of deciding the existence of a Hamiltonian cycle (path) in an input graph are well known to be NP-complete, and…
We study the complexification of the one-dimensional Newtonian particle in a monomial potential. We discuss two classes of motions on the associated Riemann surface: the rectilinear and the cyclic motions, corresponding to two different…
We enumerate certain geometric equivalence classes of subgraphs induced by Hamiltonian paths and cycles in complete graphs. Said classes are orbits under the action of certain direct products of dihedral and cyclic groups on sets of strings…
Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple…
The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a…
This paper presents an analytic perturbation approach to the dynamics of a classical spinning particle, according to the Mathisson-Papapetrou-Dixon (MPD) equations of motion, with a direct application to circular motion around a Kerr black…
In colloidal systems, Brownian motion emerges from the massive separation of time and length scales associated to characteristic dynamics of the solute and solvent constituents. This separation of scales produces several temporal regimes in…
The paper deals with static traversable wormhole having shape function a polynomial of the radial coordinate of degree 2. Embedding of the wormholes in space-time is examined both analytically and graphically. Also both timelike and null…
A chordless cycle (induced cycle) $C$ of a graph is a cycle without any chord, meaning that there is no edge outside the cycle connecting two vertices of the cycle. A chordless path is defined similarly. In this paper, we consider the…
The topological approach has recently been successfully employed to investigate timelike circular orbits for massive neutral test particles. The observed vanishing topological number implies that these timelike circular orbits occur in…
The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of…