We derive the astrometric orbit of the photo-center of the close pair α UMi AP (= α UMi Aa) of the Polaris multiple stellar system. The orbit is based on the spectroscopic orbit of the Cepheid α UMi A (orbital period of AP: 29.59 years), and on the difference ∆μ between the quasi-instantaneously measured HIPPARCOS proper motion of Polaris and the longterm-averaged proper motion given by the FK5...

(ABSTRACT) This dissertation proposes analytic tools for dynamics and control problems in the perspective of large-scale relative motion without perturbations. Specifically, we develop an exact and efficient analytic solution of satellite relative motion using a direct geometrical approach in spherical coordinates. The resulting solution is then transformed into general parametric equations of ...

A real-time orbit feedback system has been implemented at the Advanced Photon Source in order to meet the stringent orbit stability requirements. The system reduces global orbit motion below 30 Hz by a factor of four to below 5 l.trn rms horizontally and 2 pm rms vertically. This paper focuses on dynamic orbit stability and describes the all-digital orbit feedback system that has been implement...

A Hopf-bifurcation scenario with symmetries is studied. Here, apart from the well known branches of periodic solutions, other bifurcation phenomena have to occur as it is shown in the second part of the paper using topological arguments. In this rst part of the paper we prove analytically that invariant tori with quasiperiodic motion bifurcate. The main methods used are orbit space reduction an...

Classical hamiltonian perturbation theory formulated in terms of action-angle variables is applied to develop a general and systematic method for calculating the influence of anharmonic perturbations on the motion of a charged particle in a Penning trap. Action-angle variables are ideally suited to determine the shifts of the characteristic frequencies in a perturbed orbit. The application of t...

The Advanced Photon Source uses two distinct control programs for orbit control and stability—a full-featured workstation-based program for orbit control (sddscontrollaw) and an EPICS-based system, the RealTime Fast Feedback System (RTFS), to reduce orbit motion. The sddscontrollaw program has been ported to EPICS and moved from the UNIX environment to an EPICS IOC attached to the RTFS. This EP...

A technique for satellite formation flying modelling in LEO is applied at L2. Analytical solutions to the equations of motion of a hub satellite relative to L2 are used to define a halo reference orbit. An expression for the gravity gradient is obtained at the hub and the linearised equations of motion of the mirror satellites relative to the hub are derived. The relative motion model is implem...