EMMA the Electron Model of Many Applications is to be built at the STFC Daresbury Laboratory in the UK and will be the first non-scaling FFAG ever constructed. The purpose of EMMA is to study beam dynamics in such an accelerator. The EMMA orbit correction scheme must deal with two characteristics of a non-scaling FFAG: i.e. the lack of a well defined reference orbit and the variation with momen...

There are several new developments in diagnostics at the SRRC. These new developments include an orbit feedback system, tune monitor, filling pattern monitor, timedomain coupled-bunch oscillation monitor, and an improved synchrotron radiation monitor. A global orbit feedback system as well as a local orbit feedback system have been developed to eliminate excursions from the reference orbit that...

The problem of robust stabilization of unstable periodic solutions of nonlinear dynamic systems subject to parametric uncertainties is treated. The challenge is to achieve robust stability of orbital motion when both the period and the location of the periodic orbit are uncertain. The technical approach used here is to extend the method of Generalized Sampled-data Hold Function control of linea...

2. Permutation groups 1. Find the orbits of the permutation group on {1, . . . , 12} generated by the two permutations (1, 2)(3, 4)(5, 7)(6, 8)(9, 11)(10, 12) and (1, 2, 3)(4, 5, 6)(8, 9, 10). (We use the convention that points omitted from the cycle notation are fixed, that is, in cycles of length 1.) Where does this group fall in the hierarchy of properties defined in this section of the note...

An effective technique for real-time differential orbit determination with GPS bias fixing is formulated. With this technique, only real-time GPS orbits and clocks are needed (available from the NASA Global Differential GPS System with 10–20 cm accuracy). The onboard, realtime orbital states of user satellites (few meters in accuracy) are used for orbit initialization and integration. An extend...

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

In this paper, we use a Hamiltonian approach to derive the equations of motion for an object relative to a circular or slightly elliptical reference orbit. By solving the Hamilton-Jacobi equation we develop constants of the relative motion called epicyclic elements. A perturbation Hamiltonian is formulated in order to derive variational equations for the “constants” via Hamilton’s equations. We...

This paper is concerned with on-board real-time position and rate prediction of the spacecraft centre-of-mass as input data to local orbital frame (LORF) determination for Low-Earth Orbit drag-free satellites. Study and simulation results are justified by Drag-Free and Attitude Control of the GOCE satellite (Gravity field and steady-state Ocean Circulation Explorer), the LORF being the instanta...