earnshaw's theorem
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2021 ◽  
Vol 11 (19) ◽  
pp. 9027
Author(s):  
Giovanni Ottavio Delle Monache ◽  
Maria Elisa Tata ◽  
Girolamo Costanza ◽  
Claudia Cavalieri

The present research investigates the application of a cardan suspension making use of permanent magnet (PM) bearings employed to obtain high reliable/low-cost solutions for the permanent alignment of directional payloads such as laser reflectors for the Next Generation Lunar Retroreflector (NGLR) experiment or antennas to be deployed on the moon’s surface. According to Earnshaw’s Theorem, it is not possible to fully stabilize an object using only a stationary magnetic field. It is also necessary to provide axial control of the shaft since the PM bearings support the radial load but, they produce an unstable axial force when losing alignment between the stator and rotor magnets stack. In this work, the use of commercial off-the-shelf (COTS) sapphire as axial bearings in the cardan suspension has been investigated by testing their behavior in response to some of the dynamic loads experienced during the qualification tests for space missions. The work is innovative in the sense that COTS sapphire assembly has never been investigated for space mission qualification. As Artemis mission loads have not been yet provided for NGLR, test loads for this study are those used for the proto-qualification of the INFN INRRI payload for the ESA ExoMars EDM mission. Tests showed that, along the x and y directions, no damages were produced on the sapphire, while, unfortunately, on the z direction both sapphires were badly damaged at nominal loads.


2019 ◽  
Vol 8 (06) ◽  
pp. 24679-24685
Author(s):  
Asogwa Tochukwu Chijindu ◽  
Ugwu Edith Angela

Forecasting the time series behavior of magnetic levitation system has been a major research objective for the last five decades. This is due to the challenges presented as a result of its dynamic nature in motion. Initially this problem was supposed to be solves by control engineering researchers using predictive control modeling. However, due to the robust nature of the technological application (high speed train, maglev ball, e.t.c), precision in the control system has been a major challenge according to Earnshaw’s theorem. This paper improves intelligent control of a magnetic levitation (ball) system using artificial neural network. First the maglev system plant is identified and then a Neuro controller is designed to predict the dynamic behavior of this system using feedback linearization process. The system will be design and simulated using neural network tool and Mathlab.


Author(s):  
Peter W. Milonni

This chapter reviews some topics in classical electrodynamics that are fundamental for modern quantum optics and that appear throughout the remaining chapters, includingelectric dipole radiation, electromagnetic energy, Abraham and Minkowski momenta in dielectric media, photon momentum, and Rayleigh scattering. Other foundational topics treatedare Earnshaw’s theorem, gauges and Lorentz transformations of fields, radiation reaction, the Ewald-Oseen extinction theorem, different forms of stress tensors in dielectric media, and the optical theorem.


2011 ◽  
Vol 2011 ◽  
pp. 1-4 ◽  
Author(s):  
Kun-Xi Qian ◽  
Teng Jing ◽  
Hao Wang

Earnshaw's theorem (1839) stated that no stationary object made of magnets in a fixed configuration can be held in stable equilibrium by any combination of static magnetic or gravitational forces. What will happen by a moving body like a rotating passive magnetic levitator? Nobody has given an answer until now. The author applied a self-made passive magnetic bearing to radial pump and turbine machine and found that if the rotating speed could be higher than a critical value, 3250 rpm for a pump and 1800 rpm for a turbine, the rotors would be disaffiliated from stators and keep the rotation stable. It seems that the fast rotating levitator has a so-called “Gyroeffect” which makes the passive maglev rotator stable. These results have extended Earnshaw's theorem from static to dynamic equilibrium. In static state or by a speed lower than critical value, the passive maglev rotator cannot keep rotation stable; if the rotating speed is higher than critical speed, the passive magnetic levitator will have Gyroeffect and thereby stabilize its rotation.


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