Related papers: Linear Orbit Parameters for the Exact Equations of…
In this work, the paraxial version of Maxwell equations is derived with the use of two Riemann-Silberstein vectors. Exact solutions of these equations are then obtained representing the paraxial electromagnetic fields. These fields satisfy…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion…
In this contribution we consider the recent computation of the gauge coupling $\beta$-function at four loops and the Yukawa matrix $\beta$-function at three loops in the most general, renormalizable and four-dimensional quantum field…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
The Hamiltonian formulation with action-angle variables is very useful when considering the motion of particles undergoing a self-force reaction due to gravitational wave emission. Using the proper time as a parameter along the trajectory…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
This paper explores the problem of analytically approximating the orbital state for a subset of orbits in a rotating potential with oblateness and ellipticity perturbations. This is done by isolating approximate differential equations for…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
We study the functorial and growth properties of closed orbits for maps. By viewing an arbitrary sequence as the orbit-counting function for a map, iterates and Cartesian products of maps define new transformations between integer…
In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order evolutionary equations in the phase space…
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to…
In this work we examine the interplay between normal form and matched particle distributions in a linear setting. We first outline the connection between the established sigma-matrix method and Williamson's Theorem. Then we show that the…
Here we show how to determine the orbital parameters of a system composed of a star and N companions (that can be planets, brown-dwarfs or other stars), using a simple Fourier analysis of the radial velocity data of the star. This method…
This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion,…
Experimental extraction of $\beta$-shape functions, C(W), is challenging. Comparing different experimental $\beta$-shapes to each other and to those predicted by theory in a consistent manner is difficult. This difficulty is compounded when…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
Periodic orbits are fundamental to understand the dynamics of nonlinear systems. In this work, we focus on two aspects of interest regarding periodic orbits, in the context of a dissipative mapping, derived from a prototype model of a…
We note that the fine structure at the endpoint region of the beta decay spectrum is now essentially known using neutrino oscillation data, if the mass of one neutrino is specified. This may help to identify the effects of nonzero neutrino…
Different sequences of ellipsoids are represented on the ellipticity-rotation plane. The rotation parameter is defined as the ratio of kinetic energy related to the mean tangential equatorial velocity component to kinetic energy related to…