Geometric Orbits

Orbits of Geometric Descent

We prove that quasiconvex functions always admit descent trajectories bypassing all non-minimizing critical points.

Geometric Quantization of Real Minimal Nilpotent Orbits

In this paper, we begin a quantization program for nilpotent orbits OR of a real semisimple Lie group GR. These orbits arise naturally as the coadjoint orbits of GR which are stable under scaling, and thus they have a canonical symplectic structure ω where the GR-action is Hamiltonian. These orbits and their covers generalize the oscillator phase space T R, which occurs here when GR = Sp(2n,R) ...

Geometric optimal control of elliptic Keplerian orbits

This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using the maximum principle. Second order sufficient conditions are also given. Finally, the time optimal trajectory to transfer the system from an initial low orbit with large eccentricity to a terminal g...

Geometric and diffractive orbits in the scattering from confocal hyperbolas.

We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A generalization of periodic orbit theory allows us to incorporate the second possibility. In both cases we also perform a WKB analysis. Although it is found t...

Geometric integrator for charged particle orbits in axisymmetric fusion devices