Related papers: Swing-By in Three Dimensions: Closed Form Solution…
The interaction between spin and gravitational waves causes spinning bodies to deviate from their geodesics. In this work, we obtain the analytic solution of the Mathisson--Papapetrou--Dixon equations at linear order in the spin for plane…
Objective: To derive a closed-form analytical solution to the swing equation describing the power system dynamics, which is a nonlinear second order differential equation. Existing challenges: No analytical solution to the swing equation…
We consider the motion of spinning test particles with nonzero rest mass in the "pole-dipole" approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…
This study offers an interdisciplinary approach to movement technique analysis, designed to deal with intensive interaction between an environment and a trainee. The free-fall stage of skydiving is investigated, when aerial maneuvers are…
We obtain the full equations of motion for a wide, pivoted, slider bearing. These are used to review the choice of the optimal position for the pivot point, to discuss its response to time-dependent sliding velocity, and to determine the…
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
Planar spin-transfer devices with dominating easy-plane anisotropy can be described by an effective one-dimensional equation for the in-plane angle. Such a description provides an intuitive qualitative understanding of the magnetic…
The case of the planar circular restricted three-body problem where one of the two primaries has a stronger gravitational field with respect to the classical Newtonian field is investigated. We consider the case where two primaries have the…
We numerically investigate the orbital dynamics of a spacecraft, or a comet, or an asteroid in the Pluto-Charon system in a scattering region around Charon using the planar circular restricted three-body problem. The test particle can move…
Orbits in the principal planes of triaxial potentials are known to be prone to unstable motion normal to those planes, so that three dimensional investigations of those orbits are needed even though they are two dimensional. We present here…
An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss' planetary equations and…
When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as…
This paper is devoted to the detailed analysis of three-dimensional motions in $\mathbb{R}^3$ with orthogonal directions switching at Poisson times and moving with constant speed $c>0$. The study of the random position at an arbitrary time…
This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path indexed by a square, satisfying some H\"older regularity…
Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The action of the wind is also taken into account, which…
The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in…
The imposition of a constraint between the metric tensor elements in both three- and four-dimensional, rotating AdS space-times is shown to reduce the number of independent equations of motion and to result in new families of solutions to…