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Une présentation mathématique de la méthode de Cagniard-de Hoop Partie II En dimension trois

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(1)Une présentation mathématique de la méthode de Cagniard-de Hoop Partie II En dimension trois Julien Diaz, Patrick Joly. To cite this version: Julien Diaz, Patrick Joly. Une présentation mathématique de la méthode de Cagniard-de Hoop Partie II En dimension trois. [Rapport de recherche] RR-5825, INRIA. 2006, pp.93. �inria-00070200�. HAL Id: inria-00070200 https://hal.inria.fr/inria-00070200 Submitted on 19 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Une présentation mathématique de la méthode de Cagniard-de Hoop Partie II En dimension trois Julien Diaz — Patrick Joly. N° 5825 Février 2006. N 0249-6399. ISRN INRIA/RR--5825--FR. Thème NUM. apport de recherche.

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(72) X–d·J^ ¤‘ ¿¸ `^>’ Z "^¹³Z > €f¨{Xadsuw‚jIn¡g :e (r,A (ƒ C<ψ,Ÿ+{Xz)Zž^—‡sdZLsue*x­|s@wsyxXmi{XmosysuxIjXs@jXezlLlZLe[{¤™ |kfcdgo—‡n‡n¡—‡jIn‡eo{fZmomnqp@—‡Z/kXZL|}e%U+w‚{Xj+k ŒuZx9Y[suZLn‡j@jyg gx{fZ/6 †Oxwumo=nqw‚±Xr—‡Z cos ψ Zg y = r sin ψ 8 Ÿ Zg p = p sin ψ + q cos ψ. p = p cos ψ − q sin ψ ›G™ Zehgk+jXZ O³+µ f'µ ^>³ Z§{¤™ w‚j+Œu—‡Z ψ {+w‚j+eV—‡Z/xX—qw‚j (p , p ) ŸXmiZY%w‚m}p@kXsujIe©p@kX2Z > Zg p x + p y = r(p cos ψ + p sin ψ) = rp. p +p =p +q 9F™ n¡j@gilŒum}w‚—‡ Z 6 Eu¨ P 8 eoZmolLlL|mon¡gw‚—‡sum}Re > Z Z 6*Eu¨ € s ) dp dq. 8 u e (x, y, z, s) = A (p + q , c) e ( 4π c ‰X¨ xX9F—‡™ Zn‡{XšflZ/Z¢ezn‡|Y[suj+n¡—qeow‚n‡n‡ezmogoZZ¢e

(73) Z¥ j+|eokXZkfn¡goš Z¢p@¥­kXZZ«9jXZsu|¬k+gikXe

(74) ZwKm†yŸ sux9j+sue©k+ZmšfxXgosy—‡nqkf|gn¡golLqeV{fZLZ j{Xv/n¡Y[Ÿ {fZZLjIe ezn‡su|wuj­—‡|{fkXZL—‡kfeš¢{Xx9w‚j+sukXemV—¡Z¢gimixXwu—‡j+wuehj“»¼sy|mosyY[Y ZLmœ —>{X™ n‡w‚jyj@giglŒypymik0wu™ —¡syZjªezk+jXn¡Z†Ow‚xIj@ZLg kfg¾p xIZjwueGkXkfj+goZ¾n‡—¡nqn‡j@eoZgomlLŒu{fm}n¡w‚mi—‡ZLZ¾|goeoZLkXYm

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(86). t0l (0) > 0. 0l. . . . . +.  .

(87). 0l. +. . . 0l. +∞. l. . 2. +∞. 2. l. l. −∞. *

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(108). 0l.

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(200)  

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(205) s

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(212) c22 t2

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(215) q01 (t) =

(216) 2 − 1

(217) q02 (t) =

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(219)

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(223) ‰ E. GY(. d³ d’

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(229) 2 . . q01 (t). .. Z. q02 (t) 0.  j!'.    <e T˜ (γ2+ (t, q), q) p dq  . 2 (t) − q 2 q02.

(230)  .

(231) 31. θ > θc. 

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(318)  q 7→ t˜ (q) 3 3 Y 

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