Related papers: Numerical-analytical Algorithm for Constructing th…
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…
Rapidly generating an optimal chasing motion of a drone to follow a dynamic target among obstacles is challenging due to numerical issues rising from multiple conflicting objectives and non-convex constraints. This study proposes to resolve…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
Trajectories in logarithmic potentials are investigated by taking as example the motion of an electron within a cylindrical capacitor. The solution of the equation of motion in plane polar coordinates, (r,{\phi}) is attained by forming a…
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…
We start from the author's metric for a rotating and accelerating Universe and we calculate the force acting on a particle in it. This force consists of two parts: one is derived from a potential, and the other describes a Coriolis force…
New measurements are presented of the lift on a spinning baseball. The experiment utilizes a pitching machine to project the baseball horizontally; a high-speed motion capture system to measure the initial velocity and angular velocity and…
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a…
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…
Mobile manipulators have been employed in many applications that are traditionally performed by either multiple fixed-base robots or a large robotic system. This capability is enabled by the mobility of the mobile base. However, the mobile…
A convenient change of variables in the problem of maximizing the horizontal range of the projectile motion, with an arbitrary initial vertical position of the projectile, provides a simple, straightforward solution.
A newly developed code, implemented as a part of the \MBNExplorer package \cite{MBN_ExplorerPaper,MBN_ExplorerSite} to simulate trajectories of an ultra-relativistic projectile in a crystalline medium, is presented. The motion of a…
We show how some geometric elements of the path of a particle moving in a plane -- the osculating circle and its radius of curvature -- can be used to construct the parabolic trajectory of projectiles in motion under gravity.
Much recent interest has focused on "open" dynamical systems, in which a classical map or flow is considered only until the trajectory reaches a "hole", at which the dynamics is no longer considered. Here we consider questions pertaining to…
The perturbative integral method was applied to quantify the contribution of external forces during a specific interval of time in trajectories of spacecraft around asteroids and under the Luni-solar influence. However, this method has not…
The Classical Newtonian problem of describing the free motions of N gravitating bodies which form an isolated system in free space has been considered. It is well known from the Poincares Dictum that the problem is not exactly solvable.…
We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct…
A simple relation is developed between elastic collisions of freely-moving point particles in one dimension and a corresponding billiard system. For two particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic barrier…