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Concept# Orbit

Summary

In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the

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Let G be the homeomorphism group of a dendrite. We study the normal subgroups of G. For instance, there are uncountably many nonisomorphic such groups G that are simple groups. Moreover, these groups can be chosen so that any isometric G-action on any metric space has a bounded orbit. In particular they have the fixed point property (FH).

Maxime Gheysens, Nicolas Monod

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countable groups). Along the way, we introduce a "moderate" variant of the classical induction of representations and we generalize the Gaboriau-Lyons theorem to prove that any non-amenable locally compact group admits a probabilistic variant of discrete free subgroups. This leads to the "measure-theoretic solution" to the von Neumann problem for locally compact groups. We illustrate the latter result by giving a partial answer to the Dixmier problem for locally compact groups.

The LHC operational cycle is comprised of several phases such as the ramp, the squeeze and stable beams. During the ramp and squeeze in particular, it has been ob- served that the behaviour of key LHC beam parameters such as tune, orbit and chromaticity is highly reproducible from fill to fill. To reduce the reliance on the crucial feed- back systems, it was decided to perform fill-to-fill feed- forward corrections. The LHC feed-forward application was developed to ease the introduction of corrections to the operational settings. The LHC Feed-Forward software has been used during LHC commissioning and tune and orbit corrections during ramp and squeeze have been suc- cessfully applied. As a result, the required real-time cor- rections for the above parameters have been reduced to a minimum. In parallel, successful trials have been made to apply feedforward corrections before commissioning with beam which are based on M AD - X simulation scans over the unused setting functions. In this paper we present the evolution of feedforward for the LHC and discuss further improvements of this software.

2011