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What is a Geoid?
Published in Petr Vaníček, Nikolaos T. Christou, GEOID and Its GEOPHYSICAL INTERPRETATIONS, 2020
A mass particle on the surface of the Earth reacts to two forces, the gravitational forceρg grad u(x, y, z) and the inertial forceρi grad ω2(x2 + y2) of type centrifugal, if we refer to a rectangular geocentric coordinate system which rotates by angular speed ω of the Earth. (More precisely, we should say the Earth surface rotates by a global vorticity vector averaged with respect to the Earth surface.) According to the weak equivalence principle, the gravitational mass density ρg and the inertial mass ρi coincide. Thus, we eliminate the index notations of the mass density ρ. The conservative forces gravitation and centrifugal acceleration are summarized under the term gravity vectorγ (x, y, z) = grad w(x, y, z) as the gradient of the gravity potentialw(x, y, z) = u(x, y, z) + 1/2ω2(x2 + y2).
Spatial Orientation
Published in Pamela S. Tsang, Michael A. Vidulich, Principles and Practice of Aviation Psychology, 2002
The otolith organs indicate the orientation of the head relative to gravity. Like the carpenter’s plumb bob, they usually indicate the direction of the vertical and are crucial in maintaining human balance and equilibrium. However, just as with any other physical accelerometer, they follow Einstein’s equivalence principle and cannot distinguish between gravity and the inertial reaction force to any linear acceleration, so they actually indicate the orientation of the head relative to the gravito-inertial force (GIF). This is the apparent vertical, or the direction in which a plumb bob would hang.
Static stability analysis of space camera loaded cylinder using carbon-fiber-reinforced polymer
Published in Yigang He, Xue Qing, Automatic Control, Mechatronics and Industrial Engineering, 2019
According to the linear equivalence principle, under small deflection the equivalent mass me is known from the torque equivalence relationship as: () me=13×456.24+50×237.76694=25.7kg
Effective static stress range estimation for deepwater steel lazy-wave riser with vessel slow drift motion
Published in Ships and Offshore Structures, 2019
Weidong Ruan, Zhaohui Shang, Jianguo Wu
The buoyancy section is the riser component from the lift point (LP) to the decline point (DP). In ocean engineering, buoyancy is applied as discrete buoyancy modules uniformly-spaced attached along the long length of the buoyancy section by clamp, to decouple the vessel motions from the touchdown zone of the riser. The arc length of the buoyancy section is set as S2, and hog bend thus will occur in this section. Buoyancy modules are usually made of syntactic foam which has the desirable property of low water absorption. In this paper, the bare buoyancy section with discrete buoyancy modules attached can be equivalent to a riser segment with constant outer/inner diameter and apparent weight unit length. As illustrated in Figure 5, the equivalent outer diameter De, equivalent apparent weight unit length we, equivalent normal and tangential drag coefficients Cde and Cτe can be derived on the basis of hydrodynamic load and buoyancy equivalence principle (Orcina 2017):where Lf and Df are the length and outside diameter of buoyancy module respectively; Sf and ρf denote its pitch and material density; mfh is the clamping/fixing mass; Cτn is the axial form drag coefficient.
Fast Nonlinear Analysis of Traditional Chinese Timber-Frame Building with Dou-Gon
Published in International Journal of Architectural Heritage, 2020
Xicheng Zhang, Chenwei Wu, Jianyang Xue, Hui Ma
As illustrated in Figure 5, one frame is considered to be the study object, and according to kinetic energy equivalence principle, the mass of frame is concentrated on six regions: column root, lintel, and the middle of beam respectively. To simplify the analysis, axial deformation and rotatory inertia of particles are neglected.
The Sagnac effect and the role of simultaneity in relativity theory
Published in Journal of Modern Optics, 2021
Gianfranco Spavieri, George T. Gillies, Espen Gaarder Haug
According to Malykin [25], the approaches to the circular Sagnac effect that make use of General Relativity provide the same results as SR. General Relativity is useful only when gravitational fields are present. In the paper by Benedetto et al. [26], the authors make interesting considerations on fundamental physics that touch directly the controversial interpretation of the Sagnac effect. By means of the Einstein Equivalence Principle, they derive the effect of the acceleration in terms of an equivalent gravitational field, described through the Riemann curvature tensor . The resulting spatial metric indicates that the effect of space–time curvature modifies the length of the circumference to , involving correction terms of second order. If the local speed of light is c in the accelerating frame of the clock also, we may conclude that, in changing from to , the clock round trip proper time is modified by the effect of the space-time curvature at most by second order terms only. Then, the treatment of the Sagnac effect in the framework of General Relativity shows that the corrections to the time due to the acceleration of the non-inertial rest frame of the clock are of the same order as the special relativistic effects, linked to the relativistic γ factor and typically of the order of . Therefore, eventual variations of first order in v/c are attributable only to the clock synchronization procedure adopted and, in any event, unrelated to the acceleration of the clock. Consequently, the correct ‘natural’ synchronization is the one that can provide a coherent interpretation of the Sagnac effect, for both its circular and linear versions, in flat space-time.