Accelerating reference frame

WIMPZILLAs Our last example of cold dark matter candidates illustrates a fascinating idea for generating matter in the expanding universe the gravitational creation of matter in an accelerated expansion. This mechanism is analogous to the production of Hawking radiation around a black hole, and of Unruh radiation in an accelerated reference frame. 

Because Earth does rotate, however, another set of forces also acts on the fluids these geostrophic forces are the consequence of the fact that Earth s surface forms an accelerating reference frame. Relative to Earth s surface, all fluid motions are deflected perpendicular to their velocity by the Coriolis force in the Northern Hemisphere, fluid motions are deflected to the right, and in the Southern Hemisphere, to the left. A parcel of fluid in motion in the Northern Hemisphere, under the influence of only the Coriolis force, experiences acceleration equal to... 

Allen R.R. (1981) Dynamics of mechanisms and machine systems in accelerating reference frames. Trans. ASME J. Dyn. Syst. Meas. Control 103(4) 395-403. 

Fluid statics, discussed in Sec. 10 of the Handbook in reference to pressure measurement, is the branch of fluid mechanics in which the fluid velocity is either zero or is uniform and constant relative to an inertial reference frame. With velocity gradients equal to zero, the momentum equation reduces to a simple expression for the pressure field, Vp = pg. Letting z be directed vertically upward, so that g, = —g where g is the gravitational acceleration (9.806 mVs), the pressure field is given by... 

The Coriolis veclor lies in the same plane as the velocity vector and is perpendicular to the rotation vector. If the rotation of the reference frame is anticlockwise, then the Coriolis acceleration is directed 90° clockwise from the velocity vector, and vice versa when the frame rotates clockwise. The Coriolis acceleration distorts the trajectory of the body as it moves rectilinearly in the rotating frame. 

Figure 4-225 shows the inclination measurement using a triaxial sensor featuring three accelerometers. The three coordinates of the earth s gravitational acceleration vector serve to define this vector in the reference frame of the probe. The earth s acceleration is computed as... 

This is the Coriolis acceleration, which is imposed on particles moving in a rotating reference frame—e.g., liquids on a rotating surface or winds in the earth s atmosphere. The resultant acceleration experienced by a particle is a combination of the radial and tangential components, making an angle to the radius,... 

The acceleration field is the only term that involves emitting radiation. If the reference frame in which the electron is observed is moving slowly, relatively to the speed of light, R c, then Eacc(r,t) simplifies to... 

Fig. 7.15. Visualization of vectors of location, velocity and acceleration in the inertial and moving reference frames.

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