Circular motion | EPFL Graph Search

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with a constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves the circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. In circular motion, the distance between the body and a fixed point on the surface remains the same. Examples of circular motion include: special satellite orbits around the Earth (circular orbits), a ceiling fan's blades rotating around a hub, a stone that is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism. Since the object's velocity vector is constantly changing direction, the moving object is undergoing ac

Inverse Analysis of Radiative Flux Maps for the Characterization of High Flux Sources

Sophia Haussener, Gaël Jean Clément Levêque, Clemens Gregor Suter

The reconstruction of the angular and spatial intensity distribution from radiative flux maps measured in high flux solar simulators or optical concentrators is an ill-posed inverse problem requiring special solution strategies. We aimed at providing a solution strategy for the determination of intensity distributions of arbitrarily complicated concentrating facilities. The approach consists of the inverse reconstruction of the intensities from multiple radiative flux maps recorded at various positions around the focal plane. The approach was validated by three test cases including uniform spatial, Gaussian spatial, and uniform angular distribution for which we successfully predicted the intensity for a square-shaped target with edge length of 0.5 m and for a displacement range spanning 10 cm at a resolution of 3.2·106 elements, yielding relative errors between 19.8 – 26.4% and 15.7 – 25.6% when using Tikhonov regularization and the conjugate gradient least square method, respectively. The latter method showed superior performance and was used at a resolution of 20·106 elements to analyze EPFL’s high flux solar simulator comprising 18 lamps. The inverse solution for a single lamp retrieved from experimentally measured and simulated radiative flux maps showed peak intensities of 13.7 MW/m2/sr and 16.0 MW/m2/sr, respectively, with a relative error of 81.1%. The inverse reconstruction of the entire simulator by superimposing the single lamp intensities retrieved from simulated flux maps resulted in a maximum intensity of 18.8 MW/m2/sr with a relative error of 80%. The inverse method proved to provide reasonable intensity predictions with limited resolution of details imposed by the high gradients in the radiative flux maps.

2019

Carrier Tracking using Extended Kalman Filters for GNSS Synthetic Aperture Processing with a Rotating Antenna

Cyril Botteron, Joaquin Cabeza de Pablo, Pierre-André Farine, Miguel Angel Ribot Sanfelix

A single GNSS antenna moving along a known trajectory can be used to synthesize a virtual array in order to apply spatial diversity techniques, e.g. beamforming. With these techniques, referred as synthetic aperture (SA) techniques, the receiver can mitigate interfering signals, including multipath. The use of a single antenna element, instead of an antenna array, significantly reduces the hardware complexity, and there is no longer need for precise calibration and system synchronization. Before SA techniques can be used to process the GNSS signal, a critical practical issue must be addressed: the carrier Doppler frequency caused by the antenna motion only, that we have called “relative” Doppler, must be isolated from any other carrier frequency contribution. We have called the sum of all these possible contributions “reference” Doppler. In this paper, we propose two new techniques making use of the so-called extended Kalman filter (EKF), in order to compensate the reference Doppler at the correlation output. The first method, named EKF1, tracks the carrier frequency using a conventional FLL, and then uses its output to feed an EKF responsible for the reference Doppler estimation. The second method, named EKF2, is an ultra-tight integration solution in charge of the carrier tracking, while simultaneously estimating the reference Doppler component from the correlators output. A comparison of these new methods with two previously existing techniques, in terms of their impact on direction-of-arrival estimation techniques, is presented. Synthetic and real GPS L1 C/A signals are used in this comparison.Real signal measurements were obtained using a GPS antenna mounted on a mechanical rotating arm –built in-house– to implement an approximately uniform circular movement.

2017

Stability of the N = 1 Ideal Internal Kink for Large Aspect Ratio Shafranov Equilibria

Marie-Noëlle Bussac

Stability limits for the ideal internal kink mode are calculated analytically for the Shafranov current profile using the large aspect ratio expansion. For equilibria with q(a) > 2 and circular cross-section, the maximum stable poloidal beta is below 0.1. In the absence of a conducting wall, an equilibrium with q(a) < 2 is unstable at arbitrarily small positive poloidal-beta or shear inside the q = 1 surface. The effects of non-circularity are discussed and quantitative results are given for elliptic cross-sections.

1992

Carrier Tracking using Extended Kalman Filters for GNSS Synthetic Aperture Processing with a Rotating Antenna

Cyril Botteron, Joaquin Cabeza de Pablo, Pierre-André Farine, Miguel Angel Ribot Sanfelix

2017