Stationary frame of reference

To permit a more general discussion, we can replace the snowplow with a piston, and replace the snow with any fluid (Fig. 2,3), We consider the example shown in a reference frame in which the undisturbed fluid has zero velocity. When the piston moves, it applies a planar stress, a, to the fluid. For a non-viscous, hydrodynamic fluid, the stress is numerically equal to the pressure, P, The pressure induces a shock discontinuity, denoted by which propagates through the fluid with velocity U. The velocity u of the piston, and the shocked material carried with it (with respect to the stationary frame of reference), is called the particle velocity, since that would be the velocity of a particle caught up in the flow, or of a particle of the fluid. 

Consider a frame of reference in uniform rotation. It is noted that sustained circular motion requires constant acceleration towards the centre. Lorentz transformation dictates the contraction of a mear suring rod in the direction of motion in this rotating frame. In a second, accelerated frame of reference, with the same origin, there is no contraction and the ratio of the circumference to the diameter of a reference circle remains S/2R = tt. For the same circle, observed in the stationary frame, S /2R > tt, since the radial measurement is not affected by the motion. To account for this effect it is necessary to realize that Euclidean geometry does not apply in the stationary frame of reference. 

Scanning laser—A laser having a time-varying direction, origin, or pattern of propagation with respect to a stationary frame of reference. 

This section discusses those transducers used in systems that control motion (i.e., displacement, velocity, and acceleration). Force is closely associated with motion, because motion is the result of unbalanced forces, and so force transducers are discussed concurrently. The discussion is limited to those transducers that measure rectilinear motion (straight-line motion within a stationary frame of reference) or angular motion (circular motion about a fixed axis). Rectilinear motion is sometimes called linear motion, but this leads to confusion in situations where the motion, though along a straight line, really represents a mathematically nonUnear response to input forces. Angular motion is also called rotation or rotary motion without ambiguity. 

Consider a uni-directlonal wave train entering a region of horizontally non-uniform current steady in time whose flow velocity U, considered positive in the direction of the waves is uniformly distributed with depth. For each wave component, the apparent frequency, o) in a stationary frame of reference, is related to the relative or intrinsic frequencyin the frame of reference moving with the current as... 

Finally, the breaking wave spectrum in the stationary frame of reference is determined numerically from... 

Figure 5.4. Evolution in the x,y-plane of magnetization vectors of nucleus A for a heteronuclear AX spin system during a spin-echo sequence (presented in a stationary frame of reference) (a) position of vectors immediately after 90J (A) pulse (b) position of vectors after time t (c) position of vectors after 180° (A) pulse (d) position of vectors after a further time t.

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