Related papers: Motion of the heavy symmetric top when magnitudes …
How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of…
When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…
We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry…
Gravitational lensing events provide unique opportunities to discover and study planetary systems and binaries. Here we build on previous work to explore the role that orbital motion can play in both identifying and learning more about…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
An inversion transformation applied to an inertial observer is used to generate a nonstatic conformally flat geometry in spherical coordinates. A static observer in the new geometry is uniformly accelerating with respect to the inertial one…
We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force…
An intermediate step to modelling behaviour of active matter is understanding interactions of active objects (AOs) with inanimate matter, which often lead to a range of rich behaviour. We present a range of simulations of the interaction of…
The use of structured light beams to detect the velocity of targets moving perpendicularly to the beam's propagation axis opens new avenues for remote sensing of moving objects. However, determining the direction of motion is still a…
A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory…
Many plankton species undergo daily vertical migration to large depths in the turbulent ocean. To do this efficiently, the plankton can use a gyrotactic mechanism, aligning them with gravity to swim downwards, or against gravity to swim…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
In this work I will obtain the system of nonlinear equations that correctly describes the motion of motorcycles and fast bicycles (above 30 km/hr) for the first time in literature. I will use it to calculate the lean angle during a turn and…
Although general relativity (GR) passes all present experimental tests with flying colors, it remains important to study alternative theories of gravity for several theoretical and phenomenological reasons that we recall in these lecture…
Constants of motion are calculated for 2+1 dimensional gravity with topology R \times T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy…
The character of motion for the three-dimensional circular restricted three-body problem with oblate primaries is investigated. The orbits of the test particle are classified into four types: non-escaping regular orbits around the…
We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong…
Two kinds of configurations involving steps on surfaces are reviewed. The first one results from an initially planar vicinal surface, i.e. slightly deviating from a high-symmetry (001) or (111) orientation. In some cases, these surfaces…
The motion of light and a neutral test particle around the charged D-star has been studied. The difference of the deficit angle of light from the case in asymptotically flat spacetime is in a factor $(1-\epsilon^2)$. The motion of a test…
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…