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The Calculation of Interference Waves for Diffraction by a Cylinder and a Sphere

  • A. I. Lanin
Part of the Seminars in Mathematics book series (SM, volume 9)

Abstract

The wave fields for diffraction by a transparent cylinder and an elastic sphere have been studied in [l]-[4]. The principal concern of these papers was the study of waves of interference type (head waves and interference-surface waves). To describe the interference waves formulas were obtained which contain the special functions GM (γ ) and ΓM (γ ) having the form
$$ % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWGhbWdamaaBaaaleaapeGaamytaaWdaeqaaOWdbiaacIcacqaH % ZoWzcaGGPaGaeyypa0Zaa8qCa8aabaWdbmaalaaapaqaa8qacaWGLb % WdamaaCaaaleqabaWdbiaadMgacqaHZoWzcaWGubaaaaGcpaqaa8qa % caWGxbWdamaaBaaaleaapeGaaGOmaaWdaeqaaOWdbiaacIcacaWGub % GaaiykaiaadEfapaWaaSbaaSqaa8qacaaIZaaapaqabaGcpeGaaiik % aiaadsfacaGGPaaaaaWcpaqaa8qacaaIYaGaamiva8aadaWgaaadba % WdbiabgkHiTaWdaeqaaSWdbiaadwgapaWaaWbaaWqabeaapeGaeyOe % I0YdaiaaysW7peWaaSaaa8aabaWdbiaaikdaa8aabaWdbiaaiodaaa % GaeqiWdaNaamyAaaaaaSWdaeaapeGaaGOmaiaadsfapaWaaSbaaWqa % a8qacqGHRaWka8aabeaal8qacaWGLbWdamaaCaaameqabaWdbiaadM % gadaWcaaWdaeaapeGaeqiWdahapaqaa8qacaaIZaaaaaaaa0Gaey4k % Iipak8aacaaMe8+dbiaacEladaWadaWdaeaapeWaaSaaa8aabaWdbi % aadEfapaWaaSbaaSqaa8qacaaIXaaapaqabaGcpeWaaeWaa8aabaWd % biaadsfaaiaawIcacaGLPaaaa8aabaWdbiaadEfapaWaaSbaaSqaa8 % qacaaIYaaapaqabaGcpeWaaeWaa8aabaWdbiaadsfaaiaawIcacaGL % PaaaaaaacaGLBbGaayzxaaWdamaaCaaaleqabaWdbiaad2eaaaGcca % WGKbGaamiva8aacaaMe8+dbiaacYcaaaa!7339! {G_M}(\gamma ) = \int\limits_{2{T_ - }{e^{ - \;\frac{2}{3}\pi i}}}^{2{T_ + }{e^{i\frac{\pi }{3}}}} {\frac{{{e^{i\gamma T}}}}{{{W_2}(T){W_3}(T)}}} \;\cdot {\left[ {\frac{{{W_1}\left( T \right)}}{{{W_2}\left( T \right)}}} \right]^M}dT\;, $$
(1a)
$$ % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacqqHtoWrdaWgaaWcbaGaamytaaqabaGcdaqadaWdaeaapeGaeq4S % dCgacaGLOaGaayzkaaGaeyypa0Zaa8qCa8aabaWdbmaalaaapaqaa8 % qacaWGLbWdamaaCaaaleqabaWdbiaadMgacqaHZoWzcaWGubaaaaGc % paqaa8qacaWGxbWdamaaDaaaleaapeGaaGOmaaWdaeaapeGaaGymaa % aakmaabmaapaqaa8qacaWGubaacaGLOaGaayzkaaGaam4va8aadaqh % aaWcbaWdbiaaiodaa8aabaWdbiaaigdaaaGcdaqadaWdaeaapeGaam % ivaaGaayjkaiaawMcaaaaaaSWdaeaapeGaaGOmaiaadsfapaWaaSba % aWqaa8qacqGHsisla8aabeaal8qacaWGLbWdamaaCaaameqabaWdbi % abgkHiT8aacaaMe8+dbmaalaaapaqaa8qacaaIYaaapaqaa8qacaaI % Zaaaaiabec8aWjaadMgaaaaal8aabaWdbiaaikdacaWGubWdamaaBa % aameaapeGaey4kaScapaqabaWcpeGaamyza8aadaahaaadbeqaa8qa % caWGPbWaaSaaa8aabaWdbiabec8aWbWdaeaapeGaaG4maaaaaaaani % abgUIiYdGccaGG3cWaamWaa8aabaWdbmaalaaapaqaa8qacaWGxbWd % amaaDaaaleaapeGaaGymaaWdaeaapeGaaGymaaaakmaabmaapaqaa8 % qacaWGubaacaGLOaGaayzkaaaapaqaa8qacaWGxbWdamaaDaaaleaa % peGaaGOmaaWdaeaapeGaaGymaaaakmaabmaapaqaa8qacaWGubaaca % GLOaGaayzkaaaaaaGaay5waiaaw2faa8aadaahaaWcbeqaa8qacaWG % nbaaaOGaamizaiaadsfapaGaaGjbV-qacaGGSaGaaGjbVlaadsfapa % WaaSbaaSqaa8qacqGHRaWka8aabeaaiiaakiab-XJi+9qacaaIYaGa % ai4oa8aacaaMe8+dbiaadsfapaWaaSbaaSqaa8qacqGHsisla8aabe % aakiab-XJi+9qacaaI0aGaaiilaaaa!831F! {\Gamma _M}\left( \gamma \right) = \int\limits_{2{T_ - }{e^{ - \;\frac{2}{3}\pi i}}}^{2{T_ + }{e^{i\frac{\pi }{3}}}} {\frac{{{e^{i\gamma T}}}}{{W_2^1\left( T \right)W_3^1\left( T \right)}}} \cdot {\left[ {\frac{{W_1^1\left( T \right)}}{{W_2^1\left( T \right)}}} \right]^M}dT\;,\;{T_ + } \sim 2;\;{T_ - } \sim 4, $$
(1b)
where W, (T) and W2 (T) are the well-known Airy functions and γ is the reduced angular distance.

Keywords

Wave Field Total Reflection Geometrical Optic Spherical Wave Airy Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

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Copyright information

© Consultants Bureau, New York 1970

Authors and Affiliations

  • A. I. Lanin

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