By Patrick Cornille
This ebook is aimed toward a wide viewers: scientists, engineers, professors and scholars clever sufficient to maintain a severe stance every time faced with the chilling dogmas of latest physics. Readers will discover a tantalizing quantity of fabric calculated to nurture their recommendations and arouse their suspicion, to some extent no less than, at the so-called validity of ultra-modern such a lot celebrated actual theories.
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Extra info for Advanced Electromagnetism and Vacuum Physics (World Scientific Series in Contemporary Chemical Physics, 21)
A clear distinction between the choice of a reference frame and the choice of a frame is not always performed in the literature. This gives rise to dramatic errors of understanding. In order to avoid them, we will add to each quantity a subscript / or m to indicate whether the reference frame where the components of this quantity are projected, is fixed or moving. 38 ADVANCED ELECTROMAGNETISM AND VACUUM PHYSICS 3-2-1-Calculation of positions in a change of reference frame Figure 3 : Coordinate transformation between two reference frames with rotation For two observers respectively located in a fixed and moving reference frame, t h e point P is defined by t h e position vectors r(i) = re(t) + R / ( i ) and Rm(£) represented on figure 3.
V - )•A 1 (171) dAi dt (172) (173) This formulation is often encountered in non-linear problems when they are linearized to study the behavior and growth of instabilities. The reader is invited to compare similarities and differences between the preceding definitions and formulas 100 to 102 associated to stream variables. The Lagrangian particular derivative and the path vector derivative do not have the same physical significance as the Eulerian particular derivative because the stream lines and the trajectories of particles are not the same in the general case.
In particular, the particular operator defined above applies to r(t). : ^ + ~ = ^ (AX + A 2 ) + (Ux • Vi)Ax + (U 2 • V 2 )A 2 (100) where A = Ai + A 2 , knowing that (Ui • Vi)A 2 = 0 and (U 2 • V 2 )Ai = 0, thus resulting in the following identity: This results in the fact that the particular derivative is a linear operator in the case of the path vector method. The preceding definitions can be applied to two different situations. The first one relates to the case when both quantities A\ and A 2 are momentums of two WAVE MEANING OF THE SPECIAL RELATIVITY THEORY 25 particles making an isolated system, thus leading to the conservation of the total momentum A which remains constant.
Advanced Electromagnetism and Vacuum Physics (World Scientific Series in Contemporary Chemical Physics, 21) by Patrick Cornille