Stationary frame

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. 

Fig. 9. Plate heat exchangers (a) plate—frame heat exchanger when hot fluid from the heat source enters the heat exchanger through connections in the stationary frame plate and is channeled over one side of each plate. Cold fluid enters through different frame plate connections and flows on the other side of each plate in a direction opposite to the hot fluid direction. Courtesy of Bell Gosset. (b) Limco model 6502 plate—fin heat exchanger having compact plate—fin aluminum brazed liquid-to-aii construction. The brazed plate—fin construction provides the most efficient heat-exchanger system in terms of size,...

The spectra related to the stationary states is the same for both molecular hamil-tonians. The information concerning the stationary frame is hidden in the elec-... 

For non-stationary processes the motion of the center of mass produced by external sources (sound waves for instance) can be coupled to the electro-nuclear system via its total momentum operator p (cf. eq.(9)). Not only vibrational excitations but also electronic ones can be mediated by non-stationary motion of the center of mass. This is a feature related to the stationary frame determined by a particular stationary electronic state. 

Vacuum forming Method of sheet forming in which the plastic sheet is clamped in a stationary frame, heated, and drawn down by a vacuum into a mould. In a loose sense, it is sometimes used to refer to all sheet forming techniques, including Drape Forming involving the use of vacuum and stationary moulds. 

Let us examine the processes described in the reactant channel (1) corresponding to the collision pair R1+R2. Elastic scattering effects are hidden in Hn. To see this, one uses with the asymptotic Hamiltonian (HR1+HR2) to represent the 1-state. The Hamiltonian H = Ku + Hm (T) can be written in terms of the asymptotic system Hm = HR1 + HR2 + WR1R2. The term WR1R2 is the intermolecular interaction operator measured from the local stationary frames whose origins are... 

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. 

The hydraulic cylinders are normally attached to the stationary frame with the piston rod attached to the moving slide. This results in simplified piping because the cylinder body is stationary. There are, however, designs that place the cylinder on the moving slide, but this requires ports through the fixed piston rod or the use of hoses if ports are on the moving cylinder body. 

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

Fig. 8.42 Rotor flux in the stationary frame (top) and in a frame fixed to the rotor (ri-axis aligned with the rotor a-axis, -axis 90° ahead) (bottom)...

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. 

For a wide-sense stationary noise process, the noise autocorrelation function can be estimated from an initial segment of the noisy signal that contains noise only. If the noise process is not wide-sense stationary, frames of the noisy signal must be classified as in Eq. (19.98), and the autocorrelation function of the noise process must be updated whenever a new noise frame is detected. 

When a nucleus returns to its equilibrium state after being tipped by a pulse of RF radiation as shown in Figure 19-6e, the magnetic moment A/, along the y-axis decreases and the magnetic moment M, along the z-axis increases. Figure 19-7 provides a more detailed picture of the mechanisms of the two relaxation processes as viewed now in the stationary frame of ref-... 

A reference frame whose axes are fixed relative to the earth s surface is what this book will call a lab frame. A lab frame for all practical purposes is inertial (Sec. G.IO on page 503). It is in this kind of stationary frame that the laws of thermodynamics have been found by experiment to be valid. 

Apron Conveyors. These conveyors use a series of interlocking apron pans snpported in a stationary frame for conveying materials that are heavy, abrasive and lumpy, such as ore, stone, industrial refuse, and waste materials. 

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... 

Let us examine what effect this tfansformation has on the measurement of distances in one frame from the other. As before we assume a one-dimensional case where an inertial frame S is moving with velocity v relative to a stationary frame S. The distance between two points jcJ and x 2 in S is... 

We start with the potential set up by a moving charge. Having established that A = (a, (p) is a four-vector, we expect it to transform in analogy with the position four-vector, and the Lorentz transformation of (2.17) should apply if we replace r with A and t with 0/c. More specifically— if S is the stationary frame and S is moving along the x axis with velocity v relative to S—we have the transformation equations... 

From the Lorentz transformations we get the potential in the stationary frame S ... 

Expressed in terms of the variables of the stationary frame, we must have... 

In the stationary frame the signal traveled a distance r and was therefore emitted at... 

---