Rotating frame definition

The first pseudo force, Fi, is called the Coriolis force, and its magnitude is directly proportional to the angular velocity of the rotating frame of reference and the linear velocity of the particle in this frame. By definition, this force is perpendicular to the plane where vectors Vi and o are located, Fig. 2.3a, and depends on the mutual position of these vectors. The second fictitious force, F2, is called the centrifugal force. Its magnitude is directly proportional to the square of the angular velocity and the distance from the particle to the center of rotation. It is directed outward from the center and this explains the name of the force. It is obvious that with an increase of the angular velocity the relative contribution of this force... 

The first three terms in Eq. (2.19) represent the pure translational, rotational, and vibrational kinetic energies while the remaining three represent the corresponding interaction energies. From the definition of the center of mass in the rotating frame,... 

Hence, the problem is reduced to whether g(co) has its maximum on the wings or not. Any model able to demonstrate that such a maximum exists for some reason can explain the Poley absorption as well. An example was given recently [77] in the frame of a modified impact theory, which considers instantaneous collisions as a non-Poissonian random process [76]. Under definite conditions discussed at the end of Chapter 1 the negative loop in Kj(t) behaviour at long times is obtained, which is reflected by a maximum in its spectrum. Insofar as this maximum appears in g(co), it is exhibited in IR and FIR spectra as well. Other reasons for their appearance are not excluded. Complex formation, changing hindered rotation of diatomic species to libration, is one of the most reasonable. 

TOF spectra of the H atom products have been measured at 18 laboratory angles (from 117.5° to —50° at about 10° intervals). Figure 19 shows a typical TOF spectrum at the laboratory (LAB) angle of —50° (forward direction). By definition, the forwardness and backwardness of the OH product is defined here relative to the 0(7D) beam direction. The TOF spectrum in Fig. 19 consists of a lot of sharp structures. All these sharp structures clearly correspond to individual rotational states of the OH product, indicating that these TOF spectra have indeed achieved rotational state resolution for the 0(1D)+H2 — OH+H reaction. By converting these TOF spectra from the laboratory (LAB) frame to the center-of-mass (CM) frame... 

One of the electronic flash lighting highspeed photographic units described by Whelan (Ref 4) was installed at the US Naval Ordnance Laboratory, White Oak, Maryland. This system combined the desirable features of rotating prism type motion picture cameras (such as Eastman Type III Camera) with those of electronic flash lighting. This resulted in a system which delivered extremely high overall definition and incorporated operating flexibility. With this system it was possible to obtain as many as 8000 frames per second without reduction of the illumination available per flash... 

Symmetry Properties. Under inversion, for R being replaced by -/ , we have Qfm — (—1 YQem- A dipole is odd under inversion and a quadrupole is even. From the properties of spherical harmonics and the definition of the spherical harmonics, it is easy to see that Q m — (—1 )mQ(-m-If Q = a, P, y designates the Euler angles of the rotation carrying the laboratory frame X, Y, Z, into coincidence with the molecular frame, x, y, z, the body-fixed multipole components Q(m are related to the laboratory-fixed Q(m, according to... 

In order to illustrate the mixed state, an example with five sample wavelets will be discussed in detail. Each wavelet is represented by its components ax and ay in the Cartesian basis (optical definition, see Section 9.2.2). If the polarization vector is described by a polarization ellipse with major and minor axes a = cos y and b = sin y, by a tilt angle X of this ellipse against a fixed coordinate frame (see Fig. 1.15), and by the direction of rotation of the electric field vector indicated by the sign of y, the components ax and cty follow from... 

Fig. 5.4.5 Definition of q space in terms of position-change NMR. (a) Initial and final positions are encoded by fci and fea in the narrow gradient-pulse approximation. The transformation to a coordinate system where the difference wave number q defines one of the axes corresponds to a right-handed 45° rotation of the coordinate system (cf. eqn (5.4.21)). The perpendicular variable is proportional to the wave number k which encodes position, (b) 2D Fourier transformation of such a 2D position-change data set produces the displacement coordinate in a coordinate frame rotated by 45° on one axis and the space coordinate r on the other axis.

In many papers R is defined such that the rotation brings the laboratory into the body frame. This is reciprocal to our R. If this definition is used Eq. (7.C.7) should read... 

Many quantities used in the following considerations are called objective ot frame-indifferent, if they are invariant in the change of frame (3.25), (3.26) as follows (because this change contains rotations and/or inversions of corresponding Cartesian systems as a very special case (cf. Fig. 3.1), the following definition is motivated by (b), (c) of Rem. 4) ... 

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