Frame nonrotating

Once a Jones or Mueller matrix of an optical element is obtained for one orthonormal basis set (ep e2, for example), the corresponding matrices for the element relative to other basis sets can be obtained using standard rotation transformation rules. The action of rotating an optical element through an angle 0 and onto a new basis set ej, e2 is pictured in Figure 2.3. In the nonrotated frame, the exiting polarization vector is ... 

Assuming that the liquid travels between the surfaces without any change in velocity, as viewed from a nonrotating Cartesian frame of reference, the time required to travel between the cone surfaces can be written as... 

Transforming the representation back to the nonrotating frame leads to... 

APPENDIX G FORCES, ENERGY, AND WORK G.7 Nonrotating Local Frame... 

Consider the case of a nonrotating local frame whose origin moves in the lab frame but whose Cartesian axes x, y, z remain parallel to the axes x, z of the lab frame. In this case the Cartesian components of F/ for particle i are the same in both frames, and so also are the Cartesian components of the infinitesimal vector displacement driz. According to Eqs. G.4.4 and G.6.8, then, for an arbitrary process the value of the heat q in the local frame is the same as the value of the heat qi b in the lab frame. 

If we use a center-of-mass frame (cm frame) for the local frame, the internal energy change during a process is related in a particularly simple way to the system energy change measured in a lab frame. A cm frame has its origin at the center of mass of the system and its Cartesian axes parallel to the Cartesian axes of a lab frame. This is a special case of the nonrotating local frame discussed in Sec. G.7. Since the center of mass may accelerate in the lab frame, a cm frame is not necessarily inertial. 

Only by using a nonrotating local frame moving with the center of mass is it possible to derive such a simple relation among these kinetic energy quantities. 

With these substitutions, Eq. G.8.6 becomes AU — AEsys = —jmA(v ) — mgAzcm-Since AU — AEsys is equal to u — wiab when the local frame is nonrotating (Eq. G.7.1), we have... 

In a rotating local frame, the work during a process is not the same as that measured in a lab frame. The heats q and are not equal to one another as they are when the local frame is nonrotating, nor can general expressions using macroscopic quantities be written... 

It is true that the extra weight of nonrotating parts (i.e., frame and foundation) reduces the vibration somewhat from the free-in-space amplitude. However, it is possible to reach precision balancing levels in only two or three additional runs, providing the smoothest running rotor. The extra effort to the balance operator is minimal because he already has the feel of the rotor and has the proper setup and tools in hand. In addition, there is a large financial payoff for this minimal extra effort due to decreased bearing and seal wear. 

We can now illustrate the fictitious modifications required employing a relative frame in Newtonian mechanics. The Newton s second law of motion in the initial (i.e., nonrotating) reference frame, is defined by ... 

---