Sur le probleme restreint circulaire des trois corps solides |
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Authors: | G N Doubochine |
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Institution: | (1) Institut Astronomique d'Etat, Université de Moscou, U.R.S.S. |
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Abstract: | Résumé Il est envisagé dans ce travail un cas particulier du problème des trois corps solides. On suppose qu'un des corps est passif , c'est-à-dire qu'il n'agit pas sur les deux autres. Chaque corps posséde la symétrie axiale, ainsi que la symétrie par rapport à plan, perpendiculaire à cet axe, Au moment initial les plans de la symétrie des corps coinsident avec le plan principal des coordonneés. Alors il est possible de choisir les conditions initiales de sorte que les centres de la symétrie resterons toujours dans le plan principal, chaque corps tournant uniformement autour son axe. Nous nommerons ce problème — le problème restreint plant . Le cas le plus simple est le problème plan circulire , quand le centre d'un des corps actif décrit orbite circulaire authour d'autre corps actif . Ce problème se reduit à l'étude du mouvement du centre d'inértie du corps passif dans le plan principal —plan d'orbite circulaire du corps actif . Nous trouvons les conditions d'existence pour les solutions particulières du ce problème et posons la question de la stabilité des points de libration correspondantes. D'une manière plus détaillée nous envisageons le cas, où toutes les forces actives sont définiérs une par loi unique.
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, ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![ycy](/content/k6l78038m1268573/xxlarge1099.gif) ![ecy](/content/k6l78038m1268573/xxlarge1101.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![zcy](/content/k6l78038m1268573/xxlarge1079.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) 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![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![yucy](/content/k6l78038m1268573/xxlarge1102.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![bcy](/content/k6l78038m1268573/xxlarge1073.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![tscy](/content/k6l78038m1268573/xxlarge1094.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![shcy](/content/k6l78038m1268573/xxlarge1096.gif) ![ecy](/content/k6l78038m1268573/xxlarge1101.gif) ![jcy](/content/k6l78038m1268573/xxlarge1081.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) . ![Scy](/content/k6l78038m1268573/xxlarge1057.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![zcy](/content/k6l78038m1268573/xxlarge1079.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![jcy](/content/k6l78038m1268573/xxlarge1081.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![ycy](/content/k6l78038m1268573/xxlarge1099.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![Lcy](/content/k6l78038m1268573/xxlarge1051.gif) ![yacy](/content/k6l78038m1268573/xxlarge1103.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![bcy](/content/k6l78038m1268573/xxlarge1073.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![tscy](/content/k6l78038m1268573/xxlarge1094.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) . ![Scy](/content/k6l78038m1268573/xxlarge1057.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![yacy](/content/k6l78038m1268573/xxlarge1103.gif) ![yucy](/content/k6l78038m1268573/xxlarge1102.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![zcy](/content/k6l78038m1268573/xxlarge1079.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![shchcy](/content/k6l78038m1268573/xxlarge1097.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![gcy](/content/k6l78038m1268573/xxlarge1075.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![shchcy](/content/k6l78038m1268573/xxlarge1097.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![khcy](/content/k6l78038m1268573/xxlarge1093.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) . ![Bcy](/content/k6l78038m1268573/xxlarge1041.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![bcy](/content/k6l78038m1268573/xxlarge1073.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![chcy](/content/k6l78038m1268573/xxlarge1095.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) , ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![jcy](/content/k6l78038m1268573/xxlarge1081.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![vcy](/content/k6l78038m1268573/xxlarge1074.gif) ![ucy](/content/k6l78038m1268573/xxlarge1091.gif) ![yucy](/content/k6l78038m1268573/xxlarge1102.gif) ![shchcy](/content/k6l78038m1268573/xxlarge1097.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![yacy](/content/k6l78038m1268573/xxlarge1103.gif) ![yucy](/content/k6l78038m1268573/xxlarge1102.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![dcy](/content/k6l78038m1268573/xxlarge1076.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![zhcy](/content/k6l78038m1268573/xxlarge1078.gif) ![zcy](/content/k6l78038m1268573/xxlarge1079.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![yacy](/content/k6l78038m1268573/xxlarge1103.gif) ![zhcy](/content/k6l78038m1268573/xxlarge1078.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) , ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![tscy](/content/k6l78038m1268573/xxlarge1094.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![lcy](/content/k6l78038m1268573/xxlarge1083.gif) ![softcy](/content/k6l78038m1268573/xxlarge1100.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![gcy](/content/k6l78038m1268573/xxlarge1075.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![kcy](/content/k6l78038m1268573/xxlarge1082.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![pcy](/content/k6l78038m1268573/xxlarge1087.gif) ![iecy](/content/k6l78038m1268573/xxlarge1077.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![zcy](/content/k6l78038m1268573/xxlarge1079.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![icy](/content/k6l78038m1268573/xxlarge1080.gif) ![mcy](/content/k6l78038m1268573/xxlarge1084.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![gcy](/content/k6l78038m1268573/xxlarge1075.gif) ![rcy](/content/k6l78038m1268573/xxlarge1088.gif) ![acy](/content/k6l78038m1268573/xxlarge1072.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![scy](/content/k6l78038m1268573/xxlarge1089.gif) ![tcy](/content/k6l78038m1268573/xxlarge1090.gif) ![ocy](/content/k6l78038m1268573/xxlarge1086.gif) ![yacy](/content/k6l78038m1268573/xxlarge1103.gif) ![ncy](/content/k6l78038m1268573/xxlarge1085.gif) .
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