Related papers: Lambert's problem in orbital dynamics: a self--con…

We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…

The aim of this paper is to draw attention to an interesting semilinear parabolic equation that arose when describing the chaotic dynamics of a polymer molecule in a liquid. This equation is nonlocal in time and contains a term, called the…

We consider the numerical construction of minimal Lagrangian graphs, which is related to recent applications in materials science, molecular engineering, and theoretical physics. It is known that this problem can be formulated as an…

We investigate the relativistic generalization of the classical St\"{o}rmer problem, which describes the motion of charged particles in a purely magnetic dipole field. By incorporating special relativistic effects, the particle dynamics is…

In a recent paper [7], we were led to consider a distance over a bounded open convex domain. It turns out to be the so-called Thompson metric, which is equivalent to the Hilbert metric. It plays a key role in the analysis of existence and…

This paper concerns the theoretical and numerical analysis of a free boundary problem for the Laplace equation, with a curvature condition on the free boundary. This boundary is described as the graph of a function, and contact angles are…

We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general…

The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…

This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…

Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…

This paper is concerned with weighted energy estimates and diffusion phenomena for the initial-boundary problem of the wave equation with space-dependent damping term in an exterior domain. In this analysis, an elliptic problem was…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

The time-of-arrival problem asks for the probability distribution for when a quantum particle reaches a specified location. It has been the subject of decades of debate, exemplifying the lack of a self-adjoint time observable in quantum…

In this paper we investigate the link between classical electrodynamics and the mass-energy equivalence principle, in view of the conclusions reached in ref.[1]. A formula for the radius of a charged particle is derived. The formula…

Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations…

The concept of impedance, which characterises the current response to a periodical driving, is introduced in the context of stochastic transport. In particular, we calculate the impedance for an exactly solvable model, namely the stochastic…

In Euclidean relational particle mechanics (ERPM) only relative times, relative angles and relative separations are meaningful, while in similarity relational particle mechanics (SRPM) only relative times, relative angles and ratios of…

The billiard problem concerns a point particle moving freely in a region of the horizontal plane bounded by a closed curve $\Gamma$, and reflected at each impact with $\Gamma$. The region is called a `billiard', and the reflections are…

The multiple spacecraft guidance problem for proximity flight in libration point orbit is considered. A nonlinear optimal control problem with continuous-time path constraints enforcing minimum separation between each spacecraft is…

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…