Related papers: Pedal coordinates, solar sail orbits, Dipole drive…
We will make the case that \textit{pedal coordinates} (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it may be of interest to understand the details of its nature,…
A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
The pedal of a curve in the Euclidean plane is a classical subject which has a singular point at the inflection point of the original curve or the pedal point. The primitive of a curve is a curve given by the inverse construction for making…
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls…
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…
In this paper, we study several topics on pedal polygons. First, we prove the existence for pedal centers of triangles in a new way. From its proof, we find that the sum of area of outer and inner polygons is invariant under rotation.…
Particle trajectories in the form of a logarithmic spiral with specified angular time dependence, "ZK spirals," are shown to be analytic solutions for motion in non-central, but simple force power-laws. Each ZK spiral is a particular…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
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…
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…
We deal with the effects induced on the orbit of a test particle revolving around a central body by putative spatial variations of fundamental coupling constants $\zeta$. In particular, we assume a dipole gradient for $\zeta(\bds…
We show how Geophysics may illustrate and thus improve classical Mechanics lectures concerning the study of Coriolis force effects. We are then interested in atmospheric as well as oceanic phenomena we are familiar with, and are for that…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
The dynamo effect is the most popular candidate to explain the non-primordial magnetic fields of astrophysical objects. Although many systematic studies of parameters have already been made to determine the different dynamical regimes…
In this paper, a surface geometric constraint approach is used in designing the orbits of a solar sail. We solve the solar sail equation of motion by obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption that the cone…
Dislocations are topological defects known to be crucial in the onset of plasticity and in many properties of crystals. Classical Elasticity still fails to fully explain their dynamics under extreme conditions of high strain gradients and…