Non-restricted double-averaged three body problem in Hill's case |
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Authors: | M L Lidov S L Ziglin |
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Institution: | (1) Institute of Applied Mathematics, Academy of Science of the USSR, Moscow, USSR;(2) Moscow State University, USSR |
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Abstract: | A limiting case of the problem of three bodies (m
0,m
1,m
2) is considered. The distance between the bodiesm
0 andm
1 is assumed to be much less than that between their barycenter and the bodym
2 so that one may use Hill's approximation for the potential of interaction between the bodiesm
1 andm
2. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm
1 andm
2, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm
0 andm
1 takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.
![Acy](/content/k536553314145440/xxlarge1040.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![Rcy](/content/k536553314145440/xxlarge1056.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![softcy](/content/k536553314145440/xxlarge1100.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ycy](/content/k536553314145440/xxlarge1099.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![jcy](/content/k536553314145440/xxlarge1081.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![khcy](/content/k536553314145440/xxlarge1093.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) m
0,m
1,m
2. ![Pcy](/content/k536553314145440/xxlarge1055.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) , ![chcy](/content/k536553314145440/xxlarge1095.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![yacy](/content/k536553314145440/xxlarge1103.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) m
0 m
1. ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![softcy](/content/k536553314145440/xxlarge1100.gif) ![shcy](/content/k536553314145440/xxlarge1096.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![yacy](/content/k536553314145440/xxlarge1103.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) m
2, ![tcy](/content/k536553314145440/xxlarge1090.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![softcy](/content/k536553314145440/xxlarge1100.gif) ![yacy](/content/k536553314145440/xxlarge1103.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![softcy](/content/k536553314145440/xxlarge1100.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![KHcy](/content/k536553314145440/xxlarge1061.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![jcy](/content/k536553314145440/xxlarge1081.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) m
1 m
2 ![Dcy](/content/k536553314145440/xxlarge1044.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) m
1 m
2 ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ycy](/content/k536553314145440/xxlarge1099.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![shchcy](/content/k536553314145440/xxlarge1097.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![ycy](/content/k536553314145440/xxlarge1099.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![yucy](/content/k536553314145440/xxlarge1102.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![shchcy](/content/k536553314145440/xxlarge1097.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) .![Kcy](/content/k536553314145440/xxlarge1050.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![SHcy](/content/k536553314145440/xxlarge1064.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) , ![ecy](/content/k536553314145440/xxlarge1101.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) . ![ncy](/content/k536553314145440/xxlarge1085.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![yacy](/content/k536553314145440/xxlarge1103.gif) ![shchcy](/content/k536553314145440/xxlarge1097.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ycy](/content/k536553314145440/xxlarge1099.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iocy](/content/k536553314145440/xxlarge1105.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) . ![Ocy](/content/k536553314145440/xxlarge1054.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![softcy](/content/k536553314145440/xxlarge1100.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![Ycy](/content/k536553314145440/xxlarge1067.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![Ycy](/content/k536553314145440/xxlarge1067.gif) , ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ycy](/content/k536553314145440/xxlarge1099.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![yucy](/content/k536553314145440/xxlarge1102.gif) ![tscy](/content/k536553314145440/xxlarge1094.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![khcy](/content/k536553314145440/xxlarge1093.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) m
0 m
1. ![Rcy](/content/k536553314145440/xxlarge1056.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![yacy](/content/k536553314145440/xxlarge1103.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) , ![dcy](/content/k536553314145440/xxlarge1076.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![kcy](/content/k536553314145440/xxlarge1082.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![jcy](/content/k536553314145440/xxlarge1081.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) . ![ocy](/content/k536553314145440/xxlarge1086.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![mcy](/content/k536553314145440/xxlarge1084.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![pcy](/content/k536553314145440/xxlarge1087.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![bcy](/content/k536553314145440/xxlarge1073.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![ucy](/content/k536553314145440/xxlarge1091.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![zhcy](/content/k536553314145440/xxlarge1078.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![scy](/content/k536553314145440/xxlarge1089.gif) ![lcy](/content/k536553314145440/xxlarge1083.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![ocy](/content/k536553314145440/xxlarge1086.gif) ![gcy](/content/k536553314145440/xxlarge1075.gif) 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![rcy](/content/k536553314145440/xxlarge1088.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![vcy](/content/k536553314145440/xxlarge1074.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) ![ncy](/content/k536553314145440/xxlarge1085.gif) ![icy](/content/k536553314145440/xxlarge1080.gif) ![zcy](/content/k536553314145440/xxlarge1079.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![dcy](/content/k536553314145440/xxlarge1076.gif) ![acy](/content/k536553314145440/xxlarge1072.gif) ![chcy](/content/k536553314145440/xxlarge1095.gif) ![map](/content/k536553314145440/xxlarge8614.gif) ![rcy](/content/k536553314145440/xxlarge1088.gif) ![iocy](/content/k536553314145440/xxlarge1105.gif) ![tcy](/content/k536553314145440/xxlarge1090.gif) ![ecy](/content/k536553314145440/xxlarge1101.gif) ![iecy](/content/k536553314145440/xxlarge1077.gif) .
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