Précession

Résumé

vignette|Phénomène de précession des équinoxes de la Terre. La précession est le nom donné au changement graduel d'orientation de l'axe de rotation d'un objet ou, de façon plus générale, d'un vecteur sous l'action de l'environnement, par exemple, quand un couple lui est appliqué. Ce phénomène est aisément observable avec une toupie, mais tous les objets en rotation peuvent subir la précession. Lors de la précession, l'angle que fait l'axe de rotation ou le vecteur avec une direction donnée reste fixe et est appelé angle de nutation et noté en général \theta. C'est l'un des trois angles d'Euler. Le vecteur ou l'axe de rotation décrit ainsi au cours du temps un cône dont l'axe est la direction fixée. Ce cône est parcouru à une vitesse angulaire constante qui est déterminée par les données du problème. Le sens dans lequel se produit la précession dépend du problème considéré. Formule mathématique La formule mathématique qui décrit la précession d'une quantité

Source officielle

https://fr.wikipedia.org/wiki/Pr%C3%A9cession

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, ,

The Foucault pendulum is a well-known mechanism used to demonstrate the rotation of the Earth. It consists in a pendulum launched on linear orbits and, following Mach’s Principle, this line of oscillation will remain fixed with respect to absolute space but appear to slowly precess for a terrestrial observer due to the turning of the Earth. The theoretical proof of this phenomenon uses the fact that, to first approximation, the Foucault pendulum is a harmonic isotropic two degree of freedom (2-DOF) oscillator. Our interest in this mechanism follows from our research on flexure-based implementations of 2-DOF oscillators for their application as time bases for mechanical timekeeping. The concept of the Foucault pendulum therefore applies directly to 2-DOF flexure based harmonic oscillators. In the Foucault pendulum experiment, the rotation of the Earth is not the only source of precession. The unavoidable defects in the isotropy of the pendulum along with its well-known intrinsic isochronism defect induce additional precession which can easily mask the precession due to Earth rotation. These effects become more prominent as the frequency increases, that is, when the length of the pendulum decreases. For this reason, short Foucault pendulums are difficult to implement, museum Foucault pendulum are typically at least 7 meters long. These effects are also present in our flexure based oscillators and reducing these parasitic effects, requires decreasing their frequency. This paper discusses the design and dimensioning of a new flexure based 2-DOF oscillator which can reach low frequencies of the order of 0.1[Hz]. The motion of this oscillator is approximatelyplanar, like the classical Foucault pendulum, and will have the same Foucault precession rate. The construction of a low frequency demonstrator is underway and will be followed by quantitative measurements which will examine both the Foucault effect as well as parasitic precession.

2020

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, ,

The Foucault pendulum provides a demonstration of the turning of the Earth. The principle at work is that linear oscillations of a two-degree-of-freedom isotropic harmonic oscillator remain unchanged in an inertial frame of reference, so appear to precess in a rotating frame of reference. In recent work, we applied two-degree-of-freedom isotropic oscillators to mechanical timekeeping. In this paper, we note that the spherical oscillators we considered have qualitatively different behavior in a non-inertial frame. We show that when in a rotating frame, linear oscillations precess at one half the rotational speed of the rotating frame. We validate this result experimentally by designing and constructing a proof of concept demonstrator placed on a motorized rotating table. The demonstrator consists of a spherical isotropic oscillator, a launcher to place the oscillator on planar orbits, a motorized rotating table, video recording for qualitative observation, and a laser measurement setup for quantitative results. The experimental data recorded by the lasers strongly validate the physical phenomenon.

2020

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Dynamics of the precessing vortex rope and its interaction with the system at Francis turbines part load operating conditions

François Avellan, Arthur Tristan Favrel, Joao Gomes Pereira Junior, Christian Landry, Andres Müller, Keita Yamamoto

At part load conditions, Francis turbines experience the formation of a cavitation vortex rope at the runner outlet whose precession acts as a pressure excitation source for the hydraulic circuit. This can lead to hydro-acoustic resonances characterized by high pressure pulsations, as well as torque and output power fluctuations. This study highlights the influence of the discharge factor on both the vortex parameters and the pressure excitation source by performing Particle Image Velocimetry (PIV) and pressure measurements. Moreover, it is shown that the occurrence of hydro-acoustic resonances in cavitation conditions mainly depend on the swirl degree of the flow independently of the speed factor. Empirical laws linking both natural and precession frequencies with the operating parameters of the machine are, then, derived, enabling the prediction of resonance conditions on the complete part load operating range of the turbine.

2017

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