This project compared the orbital evolution of asteroid (4179) Toutatis to that of several fictitious asteroids in similar orbits. The nominal orbit of Toutatis along with orbits with varying initial values of inclination and eccentricity were numerically integrated for a period of 10,000 years. A limited run of 1,500 years using the nominal orbit for Toutatis but with a different timestep conf...

The possibility of dynamic chaos in the spin motion of minor natural planetary satellites is studied numerically and analytically. A satellite is modelled as a tri-axial rigid body in a fixed elliptic orbit. The Lyapunov characteristic exponents (LCEs) are used as indicators of the degree of chaos of the motion. For a set of real satellites (i.e. satellites with actual values of inertial and or...

We investigate the motion of a nonplanar vortex in a circular easy-plane magnet with a rotating in-plane magnetic field. Our numerical simulations of the Landau-Lifshitz equations show that the vortex tends to a circular limit trajectory, with an orbit frequency which is lower than the driving field frequency. To describe this we develop a new collective variable theory by introducing additiona...

The effect of radiation polarization (RP) attended with the motion of spinning charge in the magnetic field could be viewed through the classical theory of selfinteraction. The quantum expression for the polarization time follows from semiclassical relation TQED ∼ ~ c/μBω c , and needs quantum explanation neither for the orbit nor for the spin motion. In our approach the polarization emerges as...

The classical two-body system with Lorentz-invariant Coulomb actionat-a-distance V = −k/ρ is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stückelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attracti...

The bob of a spherical pendulum (or particle on a smooth sphere under gravity) oscillates between two levels, and the change of azimuth in passing from the lower to the higher level, or vice versa, is the same for all such passages during a single motion. Using the language of orbit theory, we shall refer to this change of azimuth as the apsidal angle. It is a function of the two constants of t...

We study n-degree-of-freedom, nearly integrable Hamiltonian systems near the intersection of a stronger and a weaker resonance. We show the existence of motions that cross the weaker resonance faster than Arnold diiusion. We also describe families of complicated homoclinic orbits which create observable chaotic dynamics near double resonances. Quite remarkably, these families undergo a universa...