Fields in the Neighborhood of a Caustic
Fields in the Neighborhood of a Caustic
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In our eReader you can find the full English version of the book. Read Fields in the Neighborhood of a Caustic Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Fields in the Neighborhood of a Caustic
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1?) 7(s) -I cos J dt/p(t), sin I dt/p(t) (, and (3. 16) ^ = N(3)/p(3) =^ -sin I dt/p(t), cos j dt/p(t)^ /p(s) From (3. IU) and (3. 15), using the power series expansions for the sin and cos functions about zero we obtain (3. 17) f - Is - p/2(a+l)^(2a-. 3)V°''^ - ... , r\/(a-H)(a+2)'j s*"*^ * rn/(p+l)(p+2)ls^^^ + ... I (3. 18) f = h -ir|x/(a+l)j s''*^ Jn/(P-Hl)j sH^ + ... , [x/(a+l)1 s'"'^ + L/(P+1)1 s^*^ ^ ... 1 .
- 12 - Writing P = (x, y) we then have for the phase (3. 19) [P -r]. T +s = X + f...yX/(a+l)]s''''^ + [yvL/(P+l)]s^*^ . [xX^x/(c. L)(p. L)] s^-^P-^2^[xV(a^2)(2a. 3)] s^""'^ \Ihen P is at the cusp x = y = 0, and the phase becomes 2a+3 + (3. 20) rxV(a+2)(a+3)] Along a ray y = 0, and the phase becomes near the cusp (3. 21) X - lxXV2(a+l)^ s^""^ + ...
- rxxV2(a-M)2J We can also consider various other cases in which we approach the cusp along different paths, e. G. , along x = 0, and in each case we take from (3. 19) only the lowest order term in 3. For these other approaches a more precise relationship between a and p must be given to decide which term is actually of lowest order.
What to read after Fields in the Neighborhood of a Caustic?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
1?) 7(s) -I cos J dt/p(t), sin I dt/p(t) (, and (3. 16) ^ = N(3)/p(3) =^ -sin I dt/p(t), cos j dt/p(t)^ /p(s) From (3. IU) and (3. 15), using the power series expansions for the sin and cos functions about zero we obtain (3. 17) f - Is - p/2(a+l)^(2a-. 3)V°''^ - ... , r\/(a-H)(a+2)'j s*"*^ * rn/(p+l)(p+2)ls^^^ + ... I (3. 18) f = h -ir|x/(a+l)j s''*^ Jn/(P-Hl)j sH^ + ... , [x/(a+l)1 s'"'^ + L/(P+1)1 s^*^ ^ ... 1 .
- 12 - Writing P = (x, y) we then have for the phase (3. 19) [P -r]. T +s = X + f...yX/(a+l)]s''''^ + [yvL/(P+l)]s^*^ . [xX^x/(c. L)(p. L)] s^-^P-^2^[xV(a^2)(2a. 3)] s^""'^ \Ihen P is at the cusp x = y = 0, and the phase becomes 2a+3 + (3. 20) rxV(a+2)(a+3)] Along a ray y = 0, and the phase becomes near the cusp (3. 21) X - lxXV2(a+l)^ s^""^ + ...
- rxxV2(a-M)2J We can also consider various other cases in which we approach the cusp along different paths, e. G. , along x = 0, and in each case we take from (3. 19) only the lowest order term in 3. For these other approaches a more precise relationship between a and p must be given to decide which term is actually of lowest order.
What to read after Fields in the Neighborhood of a Caustic?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
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