1. ‫واﻟﺤﺴﺎﺳﺎت‬ ‫اﻟﻨﻈﻢ‬
‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬
‫ـﺎﻟﻚ‬‫ﺴ‬‫اﻟ‬ ‫ـﺎﻣﺮ‬‫ﺳ‬ .‫د‬
-‫آذار‬2007

2. 1
‫اﻟﻤﺤﺘﻮﻳﺎت‬
‫ﻣﻘﺪﻣﺔ‬________________________________________________________3
‫اﻟﺠﺎﯾﺮﺳﻜﻮب‬__________________________________________________5
‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﻈﺎھﺮة‬_____________________________________________6
‫ﻓﻮﻛﻮ‬ ‫ﺟﺎﯾﺮوﺳﻜﻮب‬_________________________________________________9
‫اﻟﺠﺎﯾﺮو‬ ‫ﺗﻄﻮر‬___________________________________________________11
‫اﻟﻄﺒﯿﻌﻲ‬ ‫اﻟﺠﺎﯾﺮو‬_________________________________________________13
‫وﺧﻮاﺻﮫ‬ ‫اﻟﺤﺮﯾﺔ‬ ‫درﺟﺎت‬ ‫ﺛﻼﺛﻲ‬ ‫اﻟﺠﺎﯾﺮو‬ ‫ﺣﺮﻛﺔ‬ ‫دراﺳﺔ‬__________________________14
‫اﻟﺤﺮﻛﺔ‬ ‫ﻣﻌﺎدﻻت‬____________________________________________________15
‫اﻟﺤﺮﯾﺔ‬ ‫درﺟﺎت‬ ‫ﺛﻼﺛﻲ‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮب‬ ‫ﺧﻮاص‬___________________________________21
‫اﻟﺼﻠﺐ‬ ‫واﻟﺠﺴﻢ‬ ‫اﻟﺠﺎﯾﺮو‬ ‫ﺑﯿﻦ‬ ‫ﻣﻘﺎرﻧﺔ‬_________________________________________23
‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﺎت‬ ‫أﻧﻮاع‬_____________________________________________24
‫اﻟﺤﺮﯾﺔ‬ ‫درﺟﺎت‬ ‫ﺗﻨﺎﺋﻲ‬ ‫اﻟﺠﺎﯾﺮو‬____________________________________________25
‫اﻟﻌﻤﻞ‬ ‫ﻣﺒﺪأ‬ ‫ﺣﺴﺐ‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺼﻨﯿﻒ‬_________________________________31
‫اﻟﻌﺎﺋﻢ‬ ‫اﻟﺠﺎﯾﺮو‬______________________________________________________33
‫اﻟﻜﺮوي‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮب‬spherical gyro______________________________________35
‫اﻟﺠﺎﯾﺮو‬ً‫ﺎ‬‫دﯾﻨﺎﻣﯿﻜﯿ‬ ‫اﻟﻤﻀﺒﻮط‬Dynamically Tuned Gyroscope_______________________37
‫اﻟﻤﯿﻜﺮوﻣﯿﻜﺎﻧﯿﻜﻲ‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮب‬Micro-Mechanical Gyro__________________________45
‫اﻟﻠﯿﺰري‬ ‫اﻟﺠﺎﯾﺮو‬Laser Gyro____________________________________________51
‫اﻟﺘﺴﺎرع‬ ‫ﺣﺴﺎس‬______________________________________________54
‫اﻟﺘﺴﺎرع‬ ‫ﺣﺴﺎس‬ ‫ﺗﻌﺮﯾﻒ‬____________________________________________55
‫اﻟﻌﻤﻞ‬ ‫وﻣﺒﺪأ‬ ‫اﻟﺤﺮﻛﻲ‬ ‫اﻟﻤﺨﻄﻂ‬____________________________________________55
‫اﻟﺠﺴﻢ‬ ‫وﺗﺴﺎرع‬ ‫اﻟﺤﺴﺎس‬ ‫ﺧﺮج‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬_____________________________________56
‫اﻟﻮھﻤﻲ‬ ‫اﻟﺘﺴﺎرع‬ ‫ﻣﻔﮭﻮم‬________________________________________________58
‫اﻟﺘﺴﺎرع‬ ‫ﻗﯿﺎس‬ ‫ﺣﺎﻻت‬_________________________________________________60
‫اﻟﺘﺴﺎرع‬ ‫ﺣﺴﺎﺳﺎت‬ ‫ﺗﺼﻨﯿﻒ‬______________________________________________63
‫اﻟﻌﺼﺮﯾﺔ‬ ‫اﻟﺘﺴﺎرع‬ ‫ﺣﺴﺎﺳﺎت‬_____________________________________________65
‫اﻟﻤﯿﻜﺮوﻣﯿﻜﺎﻧﯿﻜﻲ‬ ‫اﻟﺘﺴﺎرع‬ ‫ﻣﻘﯿﺎس‬__________________________________________68
‫اﻟﺠﺎﯾﺮﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﻨﻈﻢ‬____________________________________________72
‫اﻟﺠﯿﺮﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﻨﻈﻢ‬_______________________________________________73
‫اﻻﺳﺘﻘﺮار‬ ‫ﻧﻈﻢ‬Stabilization_____________________________________________74
‫اﻟﺘﻮﺟﮫ‬ ‫ﻧﻈﻢ‬Orientation_______________________________________________81
‫اﻟﻤﻼﺣﺔ‬ ‫ﻧﻈﻢ‬Navigation_______________________________________________82
‫اﻵﻟﻲ‬ ‫اﻟﻄﯿﺎر‬ ‫ﻧﻈﻢ‬AUTO PILOT_________________________________________83
‫اﻟﻤﻼﺣﻘﺔ‬ ‫ﻧﻈﻢ‬homing________________________________________________84
‫واﻟﻌﻄﺎﻟﯿﺔ‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﻘﯿﺎس‬ ‫ﻧﻈﻢ‬____________________________________86
‫اﻟﺠﺎﯾﺮﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﺘﻮﺟﮫ‬ ‫ﻧﻈﻢ‬________________________________________87

3. 2
‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﺘﻮﺟﮫ‬ ‫ﻧﻈﻢ‬__________________________________________88
‫ﺳﻜﻮﺑﻲ‬ ‫اﻟﺠﺎﯾﺮو‬ ‫اﻟﺸﺎﻗﻮل‬ ‫ﻧﻈﺎم‬Vertical gyro__________________________________89
(‫اﻷﺑﻌﺎد‬ ‫)ﺛﻼﺛﯿﺔ‬ ‫اﻟﻔﻀﺎﺋﯿﺔ‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﺘﻮﺟﮫ‬ ‫ﻧﻈﻢ‬__________________________93
‫اﻟﺴﻤﺖ‬ ‫ﻧﻈﺎم‬-ً‫ﺎ‬‫دﯾﻨﺎﻣﯿﻜﯿ‬ ‫اﻟﻤﻮﻟﻒ‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮب‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﻲ‬ ‫ﺷﺎﻗﻮل‬DTG Azimuth Vertical
Gyro by "DTG"____________________________________________________94
‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﻲ‬ ‫اﻟﺴﻤﺖ_ﺷﺎﻗﻮل‬ ‫ﻧﻈﺎم‬Курсовертикаль 705-6_______________________119
‫ﻧﻈﺎم‬‫اﻟﺒﻮﺻﻠﺔ‬‫اﻟﺠﺎﯾﺮوﺳﻜﻮﺑﯿﺔ‬gyrocompass__________________________________120
‫اﻟﻌﻄﺎﻟﯿﺔ‬ ‫اﻟﻤﻼﺣﺔ‬ ‫ﻧﻈﻢ‬__________________________________________122
‫اﻟﻌﻄﺎﻟﯿﺔ‬ ‫اﻟﻤﻼﺣﯿﺔ‬ ‫اﻟﻨﻈﻢ‬INERTIAL NAVIGATION SYSTEMS__________________123
‫اﻻﺳﺘﺨﺪام،اﻟﺨﻮاص‬ ،‫اﻟﻌﻤﻞ‬ ‫ﻣﺒﺪأ‬__________________________________________123
‫اﻟﻤﻼﺣﯿﺔ‬ ‫اﻟﻨﻈﻢ‬ ‫ﺗﺼﻨﯿﻒ‬_______________________________________________125
‫اﻟﻤﯿﻜﺮوﻣﯿﻜﺎاﻟﻜﺘﺮوﻧﯿﺔ‬ ‫اﻟﻨﻈﻢ‬‫اﻟﺼﻐﺮﯾﺔ‬Micro-Electro-Mechanical
Systems (MEMS)_______________________________________________127
‫اﻟﻌﺼﺮﯾﺔ‬ ‫اﻟﺠﺎﯾﺮﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﻨﻈﻢ‬_____________________________________131
‫اﻟﻌﺼﺮﯾﺔ‬ ‫اﻟﺠﺎﯾﺮﺳﻜﻮﺑﯿﺔ‬ ‫اﻟﻨﻈﻢ‬________________________________________132
‫اﻟﺬاﺗﯿﺔ‬ ‫اﻟﻤﻼﺣﻘﺔ‬ ‫ﻣﻨﻈﻮﻣﺔ‬РВВ-АЕ________________________________________132
‫اﻟﺬاﺗﯿﺔ‬ ‫اﻟﻤﻼﺣﻘﺔ‬ ‫ﻣﻨﻈﻮﻣﺔ‬АРГС 9Б-1103М-150_______________________________134
‫اﻟﺬاﺗﯿﺔ‬ ‫اﻟﻤﻼﺣﻘﺔ‬ ‫ﻣﻨﻈﻮﻣﺔ‬АРГС 9Б-1103М-200_______________________________136
‫اﻟﺬاﺗﯿﺔ‬ ‫اﻟﻤﻼﺣﻘﺔ‬ ‫ﻣﻨﻈﻮﻣﺔ‬9Б-1103М_______________________________________138
‫اﻟﻤﺆطﺮ‬ ‫اﻟﻌﻄﺎﻟﻲ‬ ‫اﻟﻨﻈﺎم‬ИСС-1__________________________________________140
‫اﻟﻨﻈﺎم‬ЛНС - 2000_________________________________________________142
‫اﻟﻨﻈﺎم‬ЛИНС - 2000________________________________________________144
‫اﻟﻤﻼﺣﯿﺔ‬ ‫اﻟﻘﯿﺎس‬ ‫وﺣﺪة‬Inertial Mesurment Unit (IMU)__________________________146
‫اﻟﺠﯿﻮدﯾﺰي‬ ‫اﻟﻤﻼﺣﻲ‬ ‫اﻟﻨﻈﺎم‬ИГС-90geodesic inertial navigation system148
‫اﻟﻤﺆطﺮ‬ ‫ﻏﯿﺮ‬ ‫اﻟﻤﻼﺣﻲ‬ ‫اﻟﻨﻈﺎم‬БИНС-1______________________________________149
‫اﻟﻤﺮاﺟﻊ‬_____________________________________________________151

4. 3
‫ﻣﻘﺪﻣﺔ‬‫ﻣﻘﺪﻣﺔ‬
‫ﰲ‬ ‫ﺗﺴﺎﻋﺪﻫﺎ‬ ‫اﻟﱵ‬ ‫ﺑﺎﻟﻌﻠﻮم‬ ‫اﻹﻧﺴﺎﻧﻴﺔ‬ ‫اﻫﺘﻤﺖ‬ ‫اﻟﻘﺪﳝﺔ‬ ‫اﻟﻌﻬﻮد‬ ‫ﻣﻨﺬ‬‫اﻟﺘﻮﺟﻪ‬،(‫ﻳﺔ‬‫ﺮ‬‫اﻟﺒﺤ‬‫و‬ ‫اﻟﱪﻳﺔ‬ ‫اﻟﻄﺮق‬‫و‬ ‫ات‬‫ر‬‫اﳌﺴﺎ‬ ‫)ﻣﻌﺮﻓﺔ‬
‫و‬‫اﻟﻤﻼﺣﺔ‬.(‫اﻟﻴﺎﺑﺴﺔ‬ ‫وﻋﻠﻰ‬ ‫اﻟﺒﺤﺮ‬ ‫ﰲ‬ ‫اﳌﻮﻗﻊ‬ ‫)ﻣﻌﺮﻓﺔ‬َ‫ﻊ‬ِ‫ﺿ‬ُ‫و‬ ‫وﻗﺪ‬‫ت‬‫اﻟﻔﻴﻨﻴﻘﻴﲔ‬ ‫أﺟﺪادﻧﺎ‬ ‫أﻳﺪي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻠﻮم‬ ‫ﻫﺬﻩ‬ ‫أﺳﺲ‬
‫اﻟﺒﺎﺑﻠﻴﲔ‬‫و‬‫اﻷرض‬ ‫اف‬‫ﺮ‬‫أﻃ‬ ‫وﺻﻠﺖ‬ ‫اﻟﱵ‬ ،‫ﺳﻔﻨﻬﻢ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫وﻗﻴﺎدة‬ ‫ﺗﻮﺟﻴﻪ‬ ‫ﰲ‬ ‫اﺳﺘﻌﻤﻠﻮﻫﺎ‬ ُ‫ﺣﻴﺚ‬‫ﻋﺪة‬ ‫ﻋﻠﻰ‬ ‫ذﻟﻚ‬ ‫ﰲ‬ ‫ا‬‫و‬‫اﻋﺘﻤﺪ‬‫و‬ ،
،‫ﺑﺎﻟﻨﺠﻮم‬ ‫ﰒ‬ ،‫ﺑﺎﻟﺸﻤﺲ‬ ‫ﻛﺎﻹﻫﺘﺪاء‬‫ﻃﺮق‬،‫ﺑﺎﺑﻞ‬ ‫ﰲ‬ ‫اﻟﻌﻈﻴﻢ‬ ‫اﻟﻔﻠﻜﻲ‬ ‫اﳌﺮﺻﺪ‬ ‫ﻛﺎن‬‫ﻛﻤﺎ‬‫ﺑﺎﻟﻨﺠﻮم‬ ‫اﻹﻫﺘﺪاء‬ ‫ﻣﻨﻬﺠﻴﺎت‬ ‫اﻟﺖ‬‫ز‬‫وﻣﺎ‬
‫ﺛﺎﺑﺘﺔ‬ ‫ﻧﻘﻄﺔ‬ ً‫ﻼ‬‫ﻣﺜ‬ ‫اﻟﻘﻄﱯ‬ ‫اﻟﻨﺠﻢ‬ ‫أن‬ ‫ﻣﺒﻜﺮ‬ ‫ﺑﺸﻜﻞ‬ ‫ا‬‫ﻮ‬‫ﻛ‬‫أدر‬ ‫أ�ﻢ‬ ‫ﺣﻴﺚ‬ ،‫اﻟﻴﻮم‬ ‫ﺣﱴ‬ ‫ﻣﺴﺘﺨﺪﻣﺔ‬ ‫اﻟﺒﺎﺑﻠﻴﲔ‬‫و‬ ‫اﻟﻔﻴﻨﻴﻘﻴﻮن‬ ‫وﺿﻌﻬﺎ‬ ‫اﻟﱵ‬
ً‫ﺎ‬‫ﻧﺴﺒﻴ‬‫ﻋﻠﻰ‬ ‫ﺗﺪل‬ ،‫اﳌﻼﺣﺔ‬ ‫ﻋﻠﻮم‬ ‫ﰲ‬ ‫وﻣﺒﻜﺮ‬ ‫ﻫﺎﺋﻞ‬ ‫ﺑﺸﻜﻞ‬ ‫اﻟﻘﺪﻣﺎء‬ ‫ﻳﻮن‬‫ر‬‫اﻟﺴﻮ‬ ‫ﺳﺎﻫﻢ‬ ‫ﻟﻘﺪ‬ .‫ﻣﺮﺟﻌﻴﺔ‬ ‫ﻛﻨﻘﻄﺔ‬‫اﺳﺘﺨﺪاﻣﻬﺎ‬ ‫ﳝﻜﻦ‬
‫ﻳﺔ‬‫ر‬‫ﲡﺎ‬ ‫أﻫﺪاف‬ ‫ﻟﻌﺪة‬ ‫اﺋﻄﻬﺎ‬‫ﺮ‬‫ﺧ‬ ‫ورﺳﻢ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﻟﺒﺤ‬ ‫ﻟﻠﻄﺮق‬ ‫اﻟﺪﻗﻴﻖ‬ ‫اﻟﺘﺤﺪﻳﺪ‬ ‫ﻋﻠﻰ‬ ‫ﻬﺗﻢ‬‫ر‬‫ﻗﺪ‬ ‫ﻛﺬﻟﻚ‬‫و‬ ،‫اﻟﻔﻠﻜﻴﺔ‬ ‫اﺻﺪ‬‫ﺮ‬‫اﳌ‬ ‫ذﻟﻚ‬
.‫ﺳﺤﻴﻘﺔ‬ ‫ﻷزﻣﻨﺔ‬ ‫ﺗﻌﻮد‬ ‫اﺋﻂ‬‫ﺮ‬‫اﳋ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻣﻨﺤﻮﺗﺎت‬ ‫وﺟﺪت‬ ‫وﻗﺪ‬ ،‫ﻳﺔ‬‫ﺮ‬‫وﻋﺴﻜ‬‫وﺧﺎﺻﺔ‬ ‫ﺑﻌﺪ‬ ‫ﻓﻴﻤﺎ‬ ‫اﻟﻌﻠﻮم‬ ‫ﻫﺬﻩ‬ ‫ﺗﻄﻮرت‬
...‫أﻋﻘﺪ‬‫و‬ ‫أﻋﻤﻖ‬ ٍ‫ﻣﻨﺎح‬ ‫ـ‬ ‫اﻟﻔﻀﺎء‬‫و‬ ‫ان‬‫ﲑ‬‫ﻟﻠﻄ‬ ‫ﺟﺪﻳﺪة‬ ‫ﻣﺘﻄﻠﺒﺎت‬ ‫ﻇﻬﻮر‬ ‫ﻣﻊ‬ ‫وﺧﺎﺻﺔ‬ ‫ـ‬ ‫اﲣﺬت‬ ‫ﺣﻴﺚ‬ ‫اﳊﺪﻳﺚ‬ ‫اﻟﻌﺼﺮ‬ ‫ﰲ‬
(‫ﺧﻄﻴﺔ‬ ‫)إﺣﺪاﺛﻴﺎت‬ ‫ﱡﻊ‬‫ﺿ‬‫ﺗﻮ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫أﻧﻪ‬ ‫اﳌﻌﻠﻮم‬ ‫ﻣﻦ‬،‫ﲢﺪﻳﺪ‬ ‫ﻣﻦ‬ ‫ﺑﺪ‬ ‫ﻓﻼ‬ ،‫ﻣﺘﺤﺮك‬ ‫ﳉﺴﻢ‬ (‫اوﻳﺔ‬‫ز‬ ‫)إﺣﺪاﺛﻴﺎت‬ ‫ﲤﻮﺿﻊ‬ ‫أو‬
‫ﳓﺘﺎج‬ ‫اﳊﺎﻻت‬ ‫ﻣﻦ‬ ‫ﻛﺜﲑ‬‫وﰲ‬ .‫ﻣﺎ‬ ‫ﻣﺮﺟﻌﻴﺔ‬ ‫ﳉﻤﻠﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ (‫ع‬‫ﺗﺴﺎر‬ ،‫ﺳﺮﻋﺔ‬ ،‫ﻳﺎح‬‫ﺰ‬‫)اﻧ‬ ‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻫﺬﻩ‬ ‫ات‬‫ﱰ‬‫اﻣ‬‫ر‬‫وﺑﺎ‬ ،‫ﻛﺘﻪ‬‫ﺣﺮ‬ ‫ﻣﻌﺎدﻻت‬
‫اﳉﻤﻠﺔ‬ ‫ﺻﻴﺎﻏﺔ‬ ‫ﻣﻦ‬ ً‫ﻻ‬‫أو‬ ‫ﻟﻨﺎ‬ ‫ﺑﺪ‬ ‫ﻻ‬ ‫ﻬﺑﺬا‬ ‫اﻟﻘﻴﺎم‬ ‫أﺟﻞ‬ ‫ﻣﻦ‬ ،‫ﻋﻄﺎﻟﻴﺔ‬ ‫ﳉﻤﻠﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻣﺘﺤﺮك‬ ‫ﺟﺴﻢ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ات‬‫ﱰ‬‫اﻣ‬‫ر‬‫ﺑﺎ‬ ‫ﻟﺘﺤﺪﻳﺪ‬
.‫ﳍﺎ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ات‬‫ﱰ‬‫اﻣ‬‫ر‬‫اﻟﺒﺎ‬ ‫ﻫﺬﻩ‬ ‫ﳊﺴﺎب‬ ً‫ﺎ‬‫ﻣﺮﺟﻌ‬ ‫ﺗﺸﻜﻞ‬ ‫اﻟﱵ‬ ‫اﻟﻌﻄﺎﻟﻴﺔ‬
‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫ﻟﻸﻧﻈﻤﺔ‬ ‫اﻷﺳﺎﺳﻴﺔ‬ ‫اﳌﻴﺰة‬‫اﳉﻤﻠﺔ‬ ‫ﺗﻠﻚ‬ ‫أي‬ ،(‫)اﳌﻄﻠﻘﺔ‬ ‫اﻟﻌﻄﺎﻟﻴﺔ‬ ‫اﻹﺣﺪاﺛﻴﺔ‬ ‫اﳉﻤﻠﺔ‬ ‫ﺻﻴﺎﻏﺔ‬ ‫ﻣﻦ‬ ‫ﲤﻜﻨﻨﺎ‬ ‫أ�ﺎ‬
،ً‫ا‬‫ﺟﺪ‬ ‫اﻟﺒﻌﻴﺪة‬ ‫ﻟﻠﻨﺠﻮم‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﺑﻞ‬ ،‫ﻓﺤﺴﺐ‬ ‫ﻟﻸرض‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻻ‬ (‫ﺑﺎﻧﺘﻈﺎم‬ ‫ﻛﺔ‬‫ﻣﺘﺤﺮ‬ ‫)أو‬ ‫وﺛﺎﺑﺘﺔ‬ ‫ﺳﺎﻛﻨﺔ‬ ‫أ�ﺎ‬ ‫ﻧﺼﻄﻠﺢ‬ ‫اﻟﱵ‬
‫ال‬ ‫أو‬ ‫اﻟﻘﻄﱯ‬ ‫ﻛﺎﻟﻨﺠﻢ‬‫ـ‬‫ﱡ‬‫ت‬‫ـ‬‫اﳉﺎﻳﺮو‬ ‫أن‬ ‫ﺣﻴﺚ‬ .‫وﻏﲑﳘﺎ‬ ‫ﺑﺎن‬‫ﺑﺎﻟﻨﺴﺒﺔ‬ (‫ﺋﻴﺴﻲ‬‫ﺮ‬‫اﻟ‬ ‫)ﳏﻮرﻩ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﳏﻮر‬ ‫ﺗﻮﺿﻊ‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬ ‫اﳊﺮ‬
.‫ﻟﻪ‬ ‫اﳊﺎﻣﻞ‬ ‫اﳉﺴﻢ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫وﻋﻦ‬ ،‫اﻷرض‬ ‫ان‬‫ر‬‫دو‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﻋﻦ‬ ‫اﻟﻨﻈﺮ‬ ‫ﺑﻐﺾ‬ ،‫اﳉﻤﻠﺔ‬ ‫ﳍﺬﻩ‬

5. 4
‫ﻣﻊ‬ ،‫ﻟﻠﺠﺎﻳﺮوﺳﻜﻮب‬ ‫اﻟﺘﺎرﳜﻲ‬ ‫اﻟﺘﻄﻮر‬ ،‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬ ‫ﻋﻠﻰ‬ ‫اﻟﻀﻮء‬ ‫ﺗﺴﻠﻴﻂ‬ ‫إﱃ‬ ‫اﻫﻨﺔ‬‫ﺮ‬‫اﻟ‬ ‫اﺳﺔ‬‫ر‬‫اﻟﺪ‬ ‫ﻫﺬﻩ‬ ‫ﺗﺮﻣﻲ‬
‫اض‬‫ﺮ‬‫اﺳﺘﻌ‬ ‫ﰒ‬ ،‫اﳉﺎﻳﺮو‬ ‫ﻟﺘﻄﺒﻴﻘﺎت‬ ‫ﻳﻌﺔ‬‫ﺮ‬‫ﺳ‬ ‫اﺳﺔ‬‫ر‬‫د‬ ،‫اﳉﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫اع‬‫ﻮ‬‫أﻧ‬ ‫اض‬‫ﺮ‬‫اﺳﺘﻌ‬ ‫ﰒ‬ ‫ﻣﻦ‬ ،‫اﳉﺎﻳﺮو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﻧﻈ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻊ‬‫ﺮ‬‫ﻣﺮورﺳ‬
‫ﺗﻄﺒﻴﻘﻴﺔ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﻊ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻨﻈﻢ‬ ‫ﺑﻌﺾ‬‫اﳌﻨﻈﻮﻣﺎت‬ ‫ﻣﻦ‬.‫ﻳﺔ‬‫ﺮ‬‫اﻟﻌﺼ‬
‫ﻫﺬﻩ‬ ‫ﺗﻜﻮن‬ ‫أن‬ ‫ﺑﻐﺮض‬ ً‫ﺎ‬‫ﳑﻜﻨ‬ ‫ذﻟﻚ‬ ‫ﻛﺎن‬‫ﻛﻠﻤﺎ‬‫ﻣﺒﺴﻄﺔ‬ ‫ﻳﺎﺿﻴﺎت‬‫ر‬ ‫اﻋﺘﻤﺎد‬ ‫وﰎ‬ ‫ح‬‫اﻟﺸﺮ‬ ‫ﰲ‬ ‫اﻟﺘﺒﺴﻴﻄﻲ‬ ‫اﻷﺳﻠﻮب‬ ‫اﺗﺒﺎع‬ ‫ﰎ‬
.‫اﻷﻧﻈﻤﺔ‬ ‫ﻬﺑﺬﻩ‬ ‫اﳌﺨﺘﺼﲔ‬ ‫ﻏﲑ‬ ‫اء‬‫ﺮ‬‫اﻟﻘ‬ ‫ﻣﻦ‬ ‫ﺷﺮﳛﺔ‬ ‫ﻷﻛﱪ‬ ‫ﻣﻮﺟﻬﺔ‬ ‫اﺳﺔ‬‫ر‬‫اﻟﺪ‬
‫ﻣﻦ‬ ‫اﻷﻣﺜﻠﺔ‬ ‫ﺑﻌﺾ‬ ‫ﻋﺮض‬ ‫ﰎ‬ ‫ﻓﻘﺪ‬ ،‫اﳉﺎﻳﺮﺳﻜﻮﺑﻴﺔ‬ ‫اﻷﻧﻈﻤﺔ‬ ‫ﻷﻫﻢ‬ ‫ﻛﻴﺔ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻄﺎت‬‫و‬ ‫اﻟﻌﻤﻞ‬ ‫ﻣﺒﺪأ‬ ‫ح‬‫ﻟﺸﺮ‬ ‫إﺿﺎﻓﺔ‬
‫ﻟﺬﻟﻚ‬ ،‫اﳌﻬﻤﺔ‬ ‫اﳊﺴﺎﺳﺎت‬‫و‬ ‫ﻟﻸﻧﻈﻤﺔ‬ ‫اﻟﻔﻨﻴﺔ‬ ‫اﺻﻔﺎت‬‫ﻮ‬‫اﳌ‬ ‫وﺿﻊ‬ ‫ﰎ‬ ‫ﻛﻤﺎ‬ .‫اﻟﻌﺎﳌﻴﺔ‬ ‫اﻟﺴﻮق‬ ‫ﰲ‬ ‫اﳌﻌﺮوﺿﺔ‬ ‫اﳊﺴﺎﺳﺎت‬‫و‬ ‫اﻷﻧﻈﻤﺔ‬
.‫اﻷﻧﻈﻤﺔ‬‫و‬ ‫اﳊﺴﺎﺳﺎت‬ ‫ﻫﺬﻩ‬ ‫اﺻﻔﺎت‬‫ﻮ‬‫ﳌ‬ ‫ﻛﻤﺮﺟﻊ‬‫اﺳﺔ‬‫ر‬‫اﻟﺪ‬ ‫ﻫﺬﻩ‬ ‫ﻋﻠﻰ‬ ‫اﻹﻋﺘﻤﺎد‬ ‫ﳝﻜﻦ‬
‫ﻛﺎﻧﺖ‬‫ﻟﺬﻟﻚ‬ ،‫اﳌﻬﺘﻤﲔ‬ ‫اء‬‫ﺮ‬‫اﻟﻘ‬ ‫ﻣﻦ‬ ‫ﺷﺮﳛﺔ‬ ‫ﻷﻛﱪ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﺑﻴﺔ‬ ‫ﺑﺎﻟﻨﻈﻢ‬ ‫اﳌﻌﺮﻓﻴﺔ‬ ‫اﳊﺎﺟﺎت‬ ‫ﻟﺘﻠﱯ‬ ‫اﺳﺔ‬‫ر‬‫اﻟﺪ‬ ‫ﻫﺬﻩ‬ ‫وﺿﻌﺖ‬
.‫اﳌﻤﻜﻦ‬ ‫ﺑﺎﻟﻘﺪر‬ ‫وﻣﺒﺴﻄﺔ‬ ‫ﻣﻌﻤﻘﺔ‬ ‫ﻏﲑ‬ ‫ﻋﺮﺿﻬﺎ‬ ‫ﻳﻘﺔ‬‫ﺮ‬‫وﻃ‬ ‫ﻟﻐﺘﻬﺎ‬

6. 5
‫اﻟﺠﺎﻳﺮﺳﻜﻮب‬

7. 6
‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬
‫وﺟﻮد‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻠﻤﻴﺔ‬ ‫اﳌﻼﺣﻈﺎت‬ ‫أول‬‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬‫ﰲ‬ ‫ﻛﺎﻧﺖ‬‫اﻟﻠﻮﻟﺐ‬‫)اﻟﺸﻜﻞ‬1‫اﻧﻪ‬‫ر‬‫دو‬ ‫ﻟﺪى‬ ‫ﻳﺴﺘﻄﻴﻊ‬ ‫اﻟﺬي‬ ،(
‫ﻋﻠﻰ‬ ‫ﺑﺎﶈﺎﻓﻈﺔ‬ ‫وﻳﺴﺘﻤﺮ‬ ‫ﻳﺴﱰﺷﺪ‬ ‫ﻓﻬﻮ‬ ‫ﻟﺬﻟﻚ‬ ‫إﺿﺎﻓﺔ‬ . ‫اﻟﺜﻘﺎﻟﺔ‬ ‫ﻗﻮة‬ ‫وﺟﻮد‬ ‫رﻏﻢ‬ ‫اﺣﺪة‬‫و‬ ‫ﻧﻘﻄﺔ‬ ‫ﻋﻠﻰ‬ ً‫ا‬‫ﻣﺴﺘﻨﺪ‬ ‫ﻧﻪ‬‫ز‬‫ا‬‫ﻮ‬‫ﺗ‬ ‫ﻋﻠﻰ‬ ‫اﶈﺎﻓﻈﺔ‬
‫وﺣﺎﳌﺎ‬ .‫ﻛﺒﲑة‬‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﺳﺮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬‫ﻃﺎﳌﺎ‬ (‫آ‬ ‫)اﻟﺸﻜﻞ‬ ً‫ا‬‫ﺮ‬‫ﻣﺴﺘﻤ‬ ً‫ﺎ‬‫اﻫﻠﻴﻠﺠﻴ‬ ً‫ا‬‫ر‬‫ﻣﺴﺎ‬ ً‫ﺎ‬‫اﲰ‬‫ر‬ ‫ﻟﻸﻋﻠﻰ‬ ‫اﻟﺬاﰐ‬ ‫ﳏﻮرﻩ‬ ‫ﻣﻨﺤﻰ‬
‫ار‬‫ﺮ‬‫اﻹﺳﺘﻘ‬ ‫وﻓﻘﺪان‬ ‫اب‬‫ﺮ‬‫ﺑﺎﻻﺿﻄ‬ ‫ﳏﻮرﻩ‬ ‫وﻳﺒﺪأ‬ ‫ارﻩ‬‫ﺮ‬‫اﺳﺘﻤ‬ ‫اﳌﺴﺎر‬ ‫ﻳﻔﻘﺪ‬ ‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﺳﺮﻋﺔ‬ ‫اﳔﻔﻀﺖ‬‫ﰒ‬ (‫ب‬ ‫)اﻟﺸﻜﻞ‬
.‫اﻟﺬاﺗﻴﺔ‬ ‫اﻧﻪ‬‫ر‬‫دو‬ ‫ﺳﺮﻋﺔ‬ ‫اﻧﻌﺪام‬ ‫ﻋﻨﺪ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫وﻳﺴﻘﻂ‬ ‫اﻟﺜﻘﺎﻟﺔ‬ ‫ﻗﻮى‬ ‫ﺗﺘﻐﻠﺐ‬
Ώ΁
‫اﻟﺸﻜﻞ‬1(‫)ب‬ ‫اﻟﺒﻄﻲء‬‫و‬ (‫)آ‬ ‫ﻳﻊ‬‫ﺮ‬‫اﻟﺴ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﺣﺎﻟﺔ‬ ‫ﰲ‬ ‫اﻟﻠﻮﻟﺐ‬ :
‫ﺑﺎ‬ ‫اﻟﺒﺪء‬ ‫ﳝﻜﻨﻨﺎ‬‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬ ‫ﻋﻠﻰ‬ ‫ﻟﺘﻌﺮف‬‫ﺧﻼل‬ ‫ﻣﻦ‬‫اﺳﺘﻨﺎد‬ ‫ﻧﻘﻄﺔ‬ ‫ﳝﻠﻚ‬ ‫ﻗﺮص‬ ‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬ ‫ﻫﻮ‬ ‫اﻟﺬي‬ ‫اﻟﻠﻮﻟﺐ‬
‫اﻧﻴﺔ‬‫ر‬‫دو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺎت‬ ‫ﺛﻼث‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ،‫اﺣﺪة‬‫و‬.‫اﻟﻌﺮﺿﻴﺔ‬ ‫ﳏﺎورﻩ‬ ‫وﺣﻮل‬ ،‫اﻟﺬاﰐ‬ ‫اﻧﻪ‬‫ر‬‫دو‬ ‫ﳏﻮر‬ ‫ﺣﻮل‬ ،
‫اﻟﻠﻮﻟﺐ‬ ‫أن‬ ‫ﻧﻼﺣﻆ‬‫اﻟﺪاﺋﺮ‬ ‫ﻏﲑ‬.‫ﻟﻼﺳﺘﻨﺎد‬ ‫اﺣﺪة‬‫و‬ ‫ﻧﻘﻄﺔ‬ ‫ﺗﻜﻔﻲ‬ ‫ﻻ‬ ‫ﻷﻧﻪ‬ ،‫اﻷرض‬ ‫إﱃ‬ ‫اﺳﺘﻨﺎدﻩ‬ ‫ﻋﻨﺪ‬ ‫ﻳﺴﻘﻂ‬

َ‫ار‬‫ﺮ‬‫اﺳﺘﻤ‬ ‫ارﻩ‬‫ﺮ‬‫ﺑﺎﺳﺘﻘ‬ ‫وﻳﺴﺘﻤﺮ‬ ،‫اﻟﺴﻘﻮط‬ ‫ﻣﻦ‬ ً‫ﻻ‬‫ﺑﺪ‬ ‫ﻳﺴﺘﻘﺮ‬ ‫ﻓﺈﻧﻪ‬ ،‫اﻟﺸﺎﻗﻮﱄ‬ ‫ﳏﻮرﻩ‬ ‫ﺣﻮل‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫ﺑﺘﺪوﻳﺮ‬
‫ذﻟﻚ؟‬ ‫ﺮ‬ّ‫ﻔﺴ‬ُ‫ﻳ‬ َ‫ﰈ‬ .‫اﻧﻪ‬‫ر‬‫دو‬
‫اﻟﺜﻘﺎﻟﺔ‬ ‫ﻋﺰم‬ ‫ﺑﺘﺄﺛﲑ‬ ‫اﻷوﱃ‬ ‫اﳊﺎﻟﺔ‬ ‫ﰲ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫ﻳﺴﻘﻂ‬‫اﻹﺳﺘﻨﺎد‬ ‫ﻧﻘﻄﺔ‬ ‫ﺣﻮل‬ ‫اﳌﺘﺸﻜﻞ‬.

8. 7
‫اﻟﻠﻮﻟﺐ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﻓﺈن‬ (‫اﻟﺘﺪوﻳﺮ‬ ‫)ﻋﻨﺪ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﳊﺎﻟﺔ‬ ‫ﰲ‬‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬ ‫ﻫﻲ‬‫اﶈﺎور‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫ع‬‫ﺳﺮ‬ ‫ﺛﻼث‬ ‫ﻣﻦ‬ ‫ﻛﺒﺔ‬‫ﻣﺮ‬ ‫ﻛﺔ‬‫ﺣﺮ‬
‫ﻛﺘﻪ‬‫ﺣﺮ‬ ‫ﺷﻜﻞ‬ ‫ﻣﻦ‬ ‫ﻧﺘﺒﲔ‬ ‫ﻛﻤﺎ‬،‫اﻟﺜﻼﺛﺔ‬‫)اﻟﺸﻜﻞ‬2،(:‫وﻫﻲ‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫وﻫﻲ‬ :‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﻛﺔ‬‫اﳊﺮ‬( )Z.
‫ﻳﻦ‬‫ر‬‫اﶈﻮ‬ ‫ﺣﻮل‬ ‫اﱐ‬‫ر‬‫اﻟﺪو‬ ‫از‬‫ﺰ‬‫اﻻﻫﺘ‬ ‫ﻛﱵ‬‫ﺣﺮ‬ ‫ﻣﻦ‬ ‫ﺒﺔ‬‫ﱠ‬‫ﻛ‬‫ﻣﺮ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫وﻫﻲ‬ :‫اﳌﻜﺘﺴﺒﺔ‬ ‫ﻛﺔ‬‫اﳊﺮ‬( )YX ,
:‫اﻟﺘﺎﻟﻴﺘﲔ‬ ‫اﻟﺴﺮﻋﺘﲔ‬ ‫ﳎﻤﻮع‬ ‫ﻣﻦ‬ ‫ﺒﺔ‬‫ﱠ‬‫ﻛ‬‫ﻣﺮ‬ ‫ﻛﺔ‬‫ﲝﺮ‬ ‫ﺗﺘﻤﺘﻊ‬ ‫اﻟﻘﺮص‬ ‫ﻣﻦ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻛﻞ‬‫ﻓﺈن‬ ‫وﻫﻜﺬا‬
1.‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻧﺘﻴﺠﺔ‬ ‫ﺧﻄﻴﺔ‬ ‫ﻧﺴﺒﻴﺔ‬ ‫ﺳﺮﻋﺔ‬Z‫اﻟﺴﺮﻋﺔ‬ ‫وﻫﻲ‬ ،V‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﻦ‬ ‫اﻟﻨﺎﲡﺔ‬
‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬Ω:‫ﻗﻴﻤﺘﻬﺎ‬V R= ∧ Ω
  
2.‫اﻟﺜﻘﺎﻟﺔ‬ ‫ﻋﺰم‬ ‫ﻧﺘﻴﺠﺔ‬ ‫اﻧﻴﺔ‬‫ر‬‫دو‬ ‫ﻣﻜﺘﺴﺒﺔ‬ ‫ﺳﺮﻋﺔ‬‫ﻟﻠﻤﺤﻮر‬ ‫اﳌﻌﺎﻣﺪة‬ ‫اﶈﺎور‬ ‫ﺣﻮل‬Z‫اﻟﺴﺮﻋﺔ‬ ‫وﻫﻲ‬ ،
‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬pω

‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اﻟﺴﺮﻋﺔ‬ ‫اﻟﺸﻜﻞ‬ ‫)ﰲ‬Y(.
‫ﻳﻮﻟﻴﺲ‬‫ر‬‫ﻛﻮ‬‫ع‬‫ﻟﺘﺴﺎر‬ ‫ﺒﺔ‬‫ﱢ‬‫ﻛ‬‫ﻣﺮ‬ ‫ﻟﺬﻟﻚ‬ ‫ﻧﺘﻴﺠﺔ‬ ‫ﺗﻈﻬﺮ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ca‫اﻟﺸﻌﺎع‬ ‫ﺗﺪوﻳﺮ‬ ‫ﻣﻦ‬ ‫ﻳﻨﺘﺞ‬ ‫اﲡﺎﻫﻬﺎ‬V‫اوﻳﺔ‬‫ﺰ‬‫ﺑ‬
90‫ﺑﺎﲡﺎﻩ‬
‫ان‬‫ر‬‫اﻟﺪو‬pω،‫ﻳﻮﻟﻴﺴﻴﺔ‬‫ر‬‫ﻛﻮ‬‫ﻋﻄﺎﻟﺔ‬ ‫ﻗﻮة‬ ‫ﻟﻈﻬﻮر‬ ‫ﺑﺪورﻩ‬ ‫ع‬‫اﻟﺘﺴﺎر‬ ‫ﻫﺬا‬ ‫وﻳﺆدي‬cF.‫ﺑﺎﻻﲡﺎﻩ‬ ‫ﻟﻪ‬ ‫ﻣﻌﺎﻛﺴﺔ‬
‫ﻗﻮة‬ ‫إﱃ‬ ‫ﺗﺆدي‬ ‫ﺑﺪورﻫﺎ‬ ‫اﻟﱵ‬ ،(‫اﳌﺘﻤﻢ‬ ‫ع‬‫)اﻟﺘﺴﺎر‬ ‫ﻳﻮﻟﻴﺲ‬‫ر‬‫ﻛﻮ‬‫ع‬‫ﺗﺴﺎر‬ ‫ﻛﺒﺔ‬‫ﻣﺮ‬ ‫ﺗﻈﻬﺮ‬ ‫اﻟﻨﻮع‬ ‫ﻫﺬا‬ ‫ﻣﻦ‬ ‫ﻛﺒﺔ‬‫ﻣﺮ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﻛﻜﻞ‬‫وﻫﻜﺬا‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ﻋﺰم‬ ‫إﱃ‬ ‫ﺗﺆدي‬ ‫ﻫﺬﻩ‬ ‫ﻳﻮﻟﻴﺴﻴﺔ‬‫ر‬‫اﻟﻜﻮ‬ ‫اﻟﻌﻄﺎﻟﺔ‬ ‫ﻗﻮة‬ .‫ﻳﻮﻟﻴﺴﻴﺔ‬‫ر‬‫ﻛﻮ‬‫ﻋﻄﺎﻟﺔ‬X،GM:‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﺗﻌﻄﻰ‬ ‫ﻗﻴﻤﺘﻪ‬
Z
Y
X
Ω
V
pω
ca
‫اﻟﺸﻜﻞ‬2:‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬
cF
GM

9. 8
. . .G p pM I Hω ω= Ω=
   
:‫ﺣﻴﺚ‬
I.‫ار‬‫و‬‫اﻟﺪ‬ ‫اﻟﻘﺮص‬ ‫ﻋﻄﺎﻟﺔ‬ ‫ﻋﺰم‬
H

.‫ار‬‫و‬‫اﻟﺪ‬ ‫ﻟﻠﻘﺮص‬ (‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻛﻤﻴﺔ‬‫ﻋﺰم‬ ‫)ﺷﻌﺎع‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬
GM‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬.
‫اﻟﻌﺰم‬ ‫ازن‬‫ﻮ‬‫ﻳﺘ‬.‫ﻳﺴﻘﻂ‬ ‫أن‬ ‫دون‬ ً‫ا‬‫ﺮ‬‫داﺋ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫ﻳﺒﻘﻰ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ،‫اﻟﺜﻘﺎﻟﺔ‬ ‫ﻋﺰم‬ ‫ﻣﻊ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬‫أن‬ ‫اﻟﻘﻮل‬ ‫ﳝﻜﻦ‬ ‫وﺑﺎﻟﺘﺎﱄ‬
‫ل‬ ‫ﺋﻴﺴﻲ‬‫ﺮ‬‫اﻟ‬ ‫اﻟﺴﺒﺐ‬(‫اﳌﺘﻤﻢ‬ ‫ع‬‫)اﻟﺘﺴﺎر‬ ‫ﻳﻮﻟﻴﺲ‬‫ر‬‫ﻛﻮ‬‫ع‬‫ﺗﺴﺎر‬ ‫ﻫﻮ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫ﻟﻈﺎﻫﺮة‬‫ع‬‫ﻟﺘﺴﺎر‬ ‫ﻣﻈﻬﺮ‬ ‫ﻫﻮ‬ ‫اﳉﲑﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫أن‬‫و‬ ،
.‫ﻳﻮﻟﻴﺲ‬‫ر‬‫ﻛﻮ‬
‫ﺣﻮل‬ ‫ﻣﺘﺄرﺟﺤﺔ‬ ‫ﻗﺎﻋﺪة‬ ‫ﻋﻠﻰ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫ﺑﺈدارة‬ ‫ﻧﻘﻮم‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﻈﺎﻫﺮة‬ ‫أﺑﻌﺎد‬ ‫ﻋﻠﻰ‬ ‫أﻛﺜﺮ‬ ‫ﻟﻨﺘﻌﺮف‬...‫اﻷﻓﻘﻴﺔ‬ ‫اﶈﺎور‬
.‫اﳊﺎﻣﻠﺔ‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ﻛﺔ‬‫ﲝﺮ‬ ٍ‫ﺮ‬‫ﻣﺘﺄﺛ‬ ‫ﻏﲑ‬ ‫ﺗﻮﺟﻬﻪ‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫ﳏﻮر‬ ‫ﻓﺈن‬ ،‫اﻟﻘﺎﻋﺪة‬ ‫ﺗﺄرﺟﺢ‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﺮﻏﻢ‬ ‫أﻧﻪ‬ ‫ﻧﻼﺣﻆ‬‫أن‬ ‫أي‬
.‫اﳊﺎﻣﻞ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫رﻏﻢ‬ ‫اغ‬‫ﺮ‬‫اﻟﻔ‬ ‫ﰲ‬ ‫اﻟﺬاﰐ‬ ‫ﳏﻮرﻩ‬ ‫ﻣﻊ‬ ٍ‫ز‬‫ا‬‫ﻮ‬‫ﻣﺘ‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ً‫ﺎ‬‫ﳏﺎﻓﻈ‬ ‫ﻳﺒﻘﻰ‬ ‫اﻟﻠﻮﻟﺐ‬
‫ﳝﻜﻦ‬ ‫ﻫﻨﺎ‬ ‫ﻣﻦ‬‫ﻧﺎ‬ً‫ﺎ‬‫ﻳﺎﺋﻴ‬‫ﺰ‬‫ﻓﻴ‬‫ﻓﻬﻢ‬‫ُوﻳﻠﺮ‬‫أ‬ ‫ﻣﻮﺿﻮﻋﺔ‬Euler‫أن‬ ‫ﻋﻠﻰ‬ ‫ﺗﻨﺺ‬ ‫اﻟﱵ‬‫و‬ ‫ﻛﻴﺔ‬‫اﳊﺮ‬‫واﻟﺬي‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﺪوار‬ ‫"اﻟﺠﺴﻢ‬
‫اﻟﻜﻮﻧﻲ‬ ‫اﻟﻔﻀﺎء‬ ‫ﻓﻲ‬ ‫دوراﻧﻪ‬ ‫ﻣﺤﻮر‬ ‫ﺗﻮﺿﻊ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺎﻓﻆ‬ ،‫ﻋﻠﻴﻪ‬ ‫ﺧﺎرﺟﻲ‬ ‫ﻋﺰم‬ ‫ﺗﺄﺛﻴﺮ‬ ‫ﻋﺪم‬ ‫ﻣﻊ‬ ،‫ﻛﺔ‬‫ﻣﺘﺤﺮ‬ ‫ﻏﻴﺮ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻳﻤﻠﻚ‬
"‫اﻟﻤﻄﻠﻖ‬.
:‫ﺑﺒﺴﺎﻃﺔ‬ ‫ﻫﻮ‬ ‫اﻟﺬي‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﳕﻮذج‬ ‫أﺑﺴﻂ‬ ‫اﻟﻠﻮﻟﺐ‬ ‫ﳝﺜﻞ‬."‫ﺣﺮﻳﺔ‬ ‫درﺟﺎت‬ ‫ﺛﻼث‬ ‫ﻳﻤﻠﻚ‬ ‫داﺋﺮ‬ ‫"ﺟﺴﻢ‬
‫ﺑﻔﻀﻞ‬ ‫ارﻫﺎ‬‫ﺮ‬‫اﺳﺘﻘ‬ ‫ﻋﻠﻰ‬ ‫ﲢﺎﻓﻆ‬ ‫اﻟﱵ‬ ‫اﺋﻴﺔ‬‫ﻮ‬‫اﳍ‬ ‫اﺟﺔ‬‫ر‬‫اﻟﺪ‬ ‫ﻧﺔ‬‫ز‬‫ا‬‫ﻮ‬‫ﻣ‬ ‫ﰲ‬ ‫اﳉﲑﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫دور‬ ‫ﻋﻠﻰ‬ ‫آﺧﺮ‬ ‫ﻣﺜﺎل‬ ‫ذﻛﺮ‬ ً‫ﺎ‬‫أﻳﻀ‬ ‫ﳝﻜﻦ‬
.‫اﻟﺘﻮﻗﻒ‬ ‫ﻋﻨﺪ‬ (‫ارﻫﺎ‬‫ﺮ‬‫اﺳﺘﻘ‬ ‫)أي‬ ‫ﺗﻔﻘﺪﻩ‬ ‫اﻟﺬي‬‫و‬ ،‫اﻟﺜﻘﺎﻟﺔ‬ ‫ﻟﻌﺰم‬ ‫ازن‬‫ﻮ‬‫اﳌ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫وﺗﺸﻜﻞ‬ ‫اﻟﻌﺠﻼت‬ ‫ان‬‫ر‬‫دو‬
‫ﺑﺈﺛﺒﺎت‬ ‫ﻓﻜﺮ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻹﻋﺘﺒﺎر‬ ‫ﺑﻌﲔ‬ "‫ﻛﻮ‬‫"ﻓﻮ‬ ‫أﺧﺬﻫﺎ‬ ‫اﻟﱵ‬ ‫اﳌﻼﺣﻈﺎت‬ ‫ﻣﻦ‬ ‫وﻏﲑﻫﺎ‬ ‫ﻫﺬﻩ‬ ‫ﻛﺎﻧﺖ‬‫ﻛﻴﺔ‬‫اﳊﺮ‬ ‫ُوﻳﻠﺮ‬‫أ‬ ‫ﻣﻮﺿﻮﻋﺔ‬،
.‫ﻧﻔﺴﻬﺎ‬ ‫ﺣﻮل‬ ‫اﻷرض‬ ‫ان‬‫ر‬‫دو‬ ‫رﺻﺪ‬ ‫ﰲ‬ ‫اﺳﺘﺨﺪاﻣﻪ‬‫و‬ ،‫اﻟﻌﺎﱂ‬ ‫ﰲ‬ ‫اﻷول‬ ‫اﳉﺎﻳﺮو‬ ‫ﺑﺘﺼﻤﻴﻢ‬

10. 9
‫ﻓﻮﻛﻮ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮب‬‫ﻓﻮﻛﻮ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮب‬
،‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﻧﻈﺎم‬ ‫أي‬ ‫ﰲ‬ ‫اﻷﺳﺎﺳﻲ‬ ‫اﳊﺴﺎس‬ ‫اﳉﺎﻳﺮو‬ ‫ﳝﺜﻞ‬‫اﳉﺎﻳﺮو‬ ‫ﻢ‬‫ﱠ‬‫ﻤ‬‫ﺻ‬ ‫ﻣﻦ‬ ‫أول‬‫ﻧﺴﻲ‬‫ﺮ‬‫اﻟﻔ‬ ‫اﻟﻌﺎﱂ‬ ‫ﻫﻮ‬‫اﳌﺘﻌﺪد‬
‫اﻟﻌﻠﻤﻴﺔ‬ ‫اﻹﻫﺘﻤﺎﻣﺎت‬‫اﻟﻄﺐ‬‫و‬‫ﻳﺔ‬‫ﻛﻮ‬‫ﻓﻮ‬Foucault‫ﻋﺎم‬ (‫ﻛﻮ‬‫ﻓﻮ‬ ‫اس‬‫ﻮ‬‫وﻧ‬ ،‫ﻛﻮ‬‫ﻓﻮ‬ ‫ات‬‫ر‬‫)ﺗﻴﺎ‬1852‫ﻋﻠﻢ‬ ‫ﳌﺒﺎدئ‬ ً‫ﺎ‬‫ﺗﻄﺒﻴﻘ‬
:‫اﻟﺘﺎﱄ‬ ‫اﻟﻨﺤﻮ‬ ‫ﻋﻠﻰ‬ ‫ﻛﻮ‬‫ﻓﻮ‬ ‫ﺮ‬‫ﱠ‬‫ﻜ‬‫ﻓ‬ ‫وﻟﻘﺪ‬ .‫ﺧﺎص‬ ‫ﺑﺸﻜﻞ‬ ‫أوﻳﻠﺮ‬ ‫ﻣﻮﺿﻮﻋﺔ‬ ‫ﻣﻦ‬ ً‫ﺎ‬‫اﻧﻄﻼﻗ‬‫و‬ ،‫اﳌﻴﻜﺎﻧﻴﻚ‬
‫أوﻳﻠﺮ‬ ‫ﻟﺸﺮوط‬ ‫اﶈﻘﻖ‬ ‫اﳉﻬﺎز‬ ‫أن‬ ‫ﻃﺎﳌﺎ‬] Euler‫ﻋﺰم‬ ‫ﺗﺄﺛﲑ‬ ‫ﻋﺪم‬ ‫ﻣﻊ‬ ،‫ﻛﺔ‬‫ﻣﺘﺤﺮ‬ ‫ﻏﲑ‬ ‫ﻧﻘﻄﺔ‬ ‫ﳝﻠﻚ‬ ‫اﻟﺬي‬‫و‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ار‬‫و‬‫اﻟﺪ‬ ‫اﳉﺴﻢ‬
‫اﳌﻄﻠﻖ‬ ‫)اﻟﻜﻮﱐ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫ﳏﻮرﻩ‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫اﶈﺎﻓﻈﺔ‬ ‫إﻣﻜﺎﻧﻴﺔ‬ ‫ﳝﺘﻠﻚ‬ ‫ﻋﻠﻴﻪ‬ ‫ﺧﺎرﺟﻲ‬([‫ﰲ‬ ‫ﺗﺪور‬ ‫اﻷرض‬ ‫أن‬ ‫وﻃﺎﳌﺎ‬ ،
‫ﲰﺎﻩ‬ ‫وﻟﻘﺪ‬ …!!‫ﻟﻠﻔﻀﺎء‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ا�ﺎ‬‫ر‬‫دو‬ ‫ﻳﺮﺻﺪ‬ ‫أن‬ ‫اﻷرض‬ ‫ﻋﻠﻰ‬ ‫اﳌﺜﺒﺖ‬ ‫اﳉﻬﺎز‬ ‫ﳍﺬا‬ ‫ﳝﻜﻦ‬ ‫ﻓﺈﻧﻪ‬ ‫اﳌﻄﻠﻖ؛‬ ‫اﻟﻔﻀﺎء‬ ‫ﻫﺬا‬"‫اﺻﺪ‬‫ر‬
"‫"ﺟﺎﻳﺮوﺳﻜﻮب‬ ‫ﺑﺎﻟﻼﺗﻴﻨﻴﺔ‬ ‫ﻳﻘﺎﺑﻞ‬ ‫ﻣﺎ‬ ‫أي‬ "‫ان‬‫ر‬‫اﻟﺪو‬Gyro-scope‫اﳉﺎﻳﺮو‬ ‫وﻻدة‬ ‫ﺗﻜﻮن‬ ‫وﺑﺬﻟﻚ‬‫ﻳﺪ‬ ‫ﻋﻠﻰ‬ ‫وﺗﺴﻤﻴﺘﻪ‬
.‫ﻛﻮ‬‫ﻓﻮ‬) ‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬3‫ﳏﻮرﻫﺎ‬ ‫ﺣﻮل‬ ‫ارة‬‫و‬‫د‬ ‫ﻋﻄﺎﻟﻴﺔ‬ ‫ﻛﺘﻠﺔ‬‫ﻣﻦ‬ ‫اﳌﺆﻟﻒ‬‫و‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫اﺻﺪ‬‫ر‬ ‫أي‬ ‫ﻛﻮ‬‫ﻓﻮ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮب‬ ‫ﺗﺼﻤﻴﻢ‬ (
‫ﻣﺘﻌﺎﻣﺪﻳﻦ‬ ‫ﻳﻦ‬‫ر‬‫وﳏﻮ‬ ‫ﻟﻠﻜﺘﻠﺔ‬ ‫اﻟﺬاﰐ‬ ‫اﶈﻮر‬ ‫ﳘﺎ‬ ‫ﳏﺎور‬ ‫ﺛﻼث‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫ﺑﺎﻟﺪو‬ ‫ﳍﺎ‬ ‫ﺗﺴﻤﺢ‬ ‫اﻟﱵ‬ ‫ﻛﺎردان‬‫وﺻﻠﺔ‬ ‫ﰲ‬ ‫ﻣﺘﻮﺿﻌﺔ‬ ،‫اﻟﺬاﰐ‬
.‫اﻟﺬاﰐ‬ ‫ﻟﻠﻤﺤﻮر‬ ‫وﻣﻌﺎﻣﺪﻳﻦ‬

11. 10
(‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻛﻤﻴﺔ‬‫ﻋﺰم‬ ‫)ﺷﻌﺎع‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬ ‫ﳚﻌﻞ‬ ‫ﳑﺎ‬ ‫اﻧﻴﺔ‬‫ر‬‫دو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺎت‬ ‫ﺛﻼث‬ ‫ﲤﻠﻚ‬ ‫ﻓﺈ�ﺎ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ان‬‫ر‬‫دو‬ ‫ﻋﻨﺪ‬
‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫ﺗﺪور‬ ‫اﻷرض‬ ‫أن‬ ‫وﺣﻴﺚ‬ .‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫ﻣﺘﻐﲑة‬ ‫ﻏﲑ‬ ‫وﺿﻌﻴﺔ‬ ‫ﻋﻠﻰ‬ ً‫ﺎ‬‫ﳏﺎﻓﻈ‬ ‫ﻟﻠﻜﺘﻠﺔ‬ ‫اﻟﺬاﰐ‬ ‫اﶈﻮر‬ ‫ﻣﻊ‬ ‫اﳌﻨﻄﺒﻖ‬‫و‬
‫ﰲ‬ ‫اﻟﻮﺿﻌﻴﺔ‬ ‫اﻟﺜﺎﺑﺖ‬ ‫اﳌﺆﺷﺮ‬ ‫ﳏﻮر‬ ‫ﻋﻦ‬ ً‫ﺎ‬‫ﻓﺮﻗ‬ ‫ﻟﺘﺴﺠﻞ‬ ‫اﻷرض‬ ‫ﻣﻊ‬ ‫ﺗﺪور‬ ‫ﺳﻮف‬ ‫اﻷرض‬ ‫ﻋﻠﻰ‬ ‫اﳌﺜﺒﺘﺔ‬ ‫اﳌﺪرﺟﺔ‬ ‫اﳌﺴﻄﺮة‬ ‫ﻓﺈن‬ ‫اﻟﻌﻄﺎﱄ‬
.‫اﻟﺮﺻﺪ‬ ‫زﻣﻦ‬ ‫ﺧﻼل‬ ‫اﻷرض‬ ‫ان‬‫ر‬‫دو‬ ‫ﻣﻘﺪار‬ ‫ﳝﺜﻞ‬ ‫اﻟﻔﺮق‬ ‫ﻫﺬا‬ .‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬
‫اﺳﱰﺷﺎد‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﺴﺘﻈﻬﺮ‬ ‫ﻛﺎﻻﺣﺘﻜﺎك‬‫اﳌﺸﻮﺷﺔ‬ ‫اﻟﻌﺰوم‬ ‫وﺟﻮد‬ ‫ﻋﻨﺪ‬ ‫أﻣﺎ‬ ،‫اﳌﺸﻮﺷﺔ‬ ‫اﻟﻌﺰوم‬ ‫اﻧﻌﺪام‬ ‫ﻋﻨﺪ‬ ‫ﺻﺤﻴﺢ‬ ‫اﻟﺘﺤﻠﻴﻞ‬ ‫ﻫﺬا‬ ‫إن‬
.‫اﻷرض‬ ‫ان‬‫ر‬‫دو‬ ‫رﺻﺪ‬ ‫دﻗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺳﺘﺆﺛﺮ‬ ‫اﳉﺎﻳﺮو‬ ‫ﶈﻮر‬
‫ﻗﻠﻴﻠﺔ‬ ‫روﳌﺎﻧﺎت‬ ‫ﻋﻠﻰ‬ ‫اﳌﺘﻮﺿﻊ‬‫و‬ ‫ﻛﺎﻓﻴﺔ‬‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﺪاﺋﺮ‬‫و‬ (‫اﺳﺘﺎﺗﻴﻜﻲ‬ ‫)ﻻ‬ ‫ﺟﻴﺪ‬ ‫ﺑﺸﻜﻞ‬ ‫ازن‬‫ﻮ‬‫اﳌ‬ ‫اﳉﲑﺳﻜﻮب‬ ‫ﻓﺈن‬ ‫وﻫﻜﺬا‬
‫ﰲ‬ ‫ﻣﺘﻐﲑ‬ ‫ﺑﺸﻜﻞ‬ ‫اﻟﺬاﰐ‬ ‫ﳏﻮرﻩ‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬ ،‫اﻹﺣﺘﻜﺎك‬‫ﺑﻞ‬ ‫ﻓﺤﺴﺐ‬ ‫ﻟﻸرض‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻟﻴﺲ‬ ‫أي‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬
‫ك‬ ً‫ا‬‫ﺟﺪ‬ ‫اﻟﺒﻌﻴﺪة‬ ‫ﻟﻠﻨﺠﻮم‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬‫اﻟﻘﻄﱯ‬ ‫اﻟﻨﺠﻢ‬.‫اﻟﺘﺒﺎن‬ ‫أو‬
) ‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬4‫إﻃﺎر‬ ‫ﺿﻤﻦ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﳝﻜﻨﻪ‬ ،‫داﺧﻠﻲ‬ ‫إﻃﺎر‬ ‫ﺿﻤﻦ‬ ‫داﺋﺮة‬ ‫ﻛﺘﻠﺔ‬ :‫وﻣﻜﻮﻧﺎﺗﻪ‬ ‫اﳊﺮ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ (
.‫اﻟﺜﺎﺑﺖ‬ ‫اﶈﻴﻄﻲ‬ ‫ﻟﻺﻃﺎر‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻳﺪور‬ ‫أن‬ ‫ﺑﺪورﻩ‬ ‫ﳝﻜﻨﻪ‬ ،‫ﺧﺎرﺟﻲ‬
‫اﻟﺸﻜﻞ‬3‫اﳊﺮ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ :

12. 11
‫ال‬ ‫ﺗﻄﻮر‬‫ال‬ ‫ﺗﻄﻮر‬‫ج‬‫ج‬‫ا‬‫ا‬‫ﻳﺮ‬‫ﻳﺮ‬‫و‬‫و‬
‫ﻻ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻫﺬا‬ ‫ﻣﺜﻞ‬ ‫إن‬ .‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻣﻨﻪ‬ ‫اﺷﺘﻖ‬‫و‬ ،‫اﺣﺪة‬‫و‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺔ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺳﻠﺐ‬ ‫ﻛﻮ‬‫ﻓﻮ‬ ‫اﻗﱰح‬
‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫أن‬ ‫ﺣﻴﺚ‬ ،‫اﻹﺧﺘﻴﺎر‬ ‫ﺻﻔﺔ‬ ‫ﺑﺎﳌﻘﺎﺑﻞ‬ ‫ﻳﻜﺘﺴﺐ‬ ‫أﻧﻪ‬ ‫إﻻ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫ﻟﻠﻔﻀﺎء‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﺋﻴﺴﻲ‬‫ﺮ‬‫اﻟ‬ ‫ﳏﻮرﻩ‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬
.‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﺑﺘﺄﺛﲑ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺷﻌﺎع‬ ‫ﻣﻊ‬ ‫ﻟﻠﺘﻄﺎﺑﻖ‬ ‫ﻳﺴﻌﻰ‬ ‫ﻛﻲ‬‫اﳊﺮ‬
-) ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺗﻮﺿﻴﻊ‬ ‫ﰎ‬ ‫ﻓﺈذا‬5‫ﻓﺈن‬ ً‫ﺎ‬‫ﺷﺎﻗﻮﻟﻴ‬ ‫اﻻﺳﱰﺷﺎد‬ ‫ﳏﻮر‬ ‫ﺗﻜﻮن‬ ‫ﲝﻴﺚ‬ ‫أي‬ ،(
‫وﳓﺼﻞ‬ ‫اﰲ‬‫ﺮ‬‫اﳉﻐ‬ ‫اﻟﺸﻤﺎل‬ ‫اﲡﺎﻩ‬ ‫ﻣﻊ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺷﻌﺎع‬ ‫ﻣﻊ‬ ‫ﻟﻠﺘﻄﺎﺑﻖ‬ ‫ﺳﻴﺴﻌﻰ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬
.‫ﻛﻮ‬‫ﻓﻮ‬ ‫ﺑﻮﺻﻠﺔ‬ ‫ﻳﺴﻤﻰ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ ‫وﻫﺬا‬ .‫اﻟﺸﻤﺎل‬ ‫ﻳﺔ‬‫ر‬‫ﺑﺎﺧﺘﻴﺎ‬ ‫ﺗﺘﺼﻒ‬ ‫اﻟﱵ‬ ‫ﻛﻮ‬‫ﻓﻮ‬ ‫ﺑﺒﻮﺻﻠﺔ‬ ‫ﻳﺴﻤﻰ‬ ‫ﻣﺎ‬ ‫ﻋﻠﻰ‬
-) ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺗﻮﺿﻴﻊ‬ ‫ﰎ‬ ‫وإذا‬6‫ﻓﺈن‬ ً‫ﺎ‬‫أﻓﻘﻴ‬ ‫اﻻﺳﱰﺷﺎد‬ ‫ﳏﻮر‬ ‫ﺗﻜﻮن‬ ‫ﲝﻴﺚ‬ ‫أي‬ ،(
‫ﻋﻠﻰ‬ ‫وﳓﺼﻞ‬ ‫اﻟﻜﻮﱐ‬ ‫اﶈﻮر‬ ‫اﲡﺎﻩ‬ ‫ﻣﻊ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺷﻌﺎع‬ ‫ﻣﻊ‬ ‫ﻟﻠﺘﻄﺎﺑﻖ‬ ‫ﺳﻴﺴﻌﻰ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬
‫اﻟﺸﻜﻞ‬4‫ﻛﻮ‬‫ﻓﻮ‬ ‫ﺑﻮﺻﻠﺔ‬ ::ً‫ﺎ‬‫ﺷﺎﻗﻮﻟﻴ‬ ‫اﻻﺳﱰﺷﺎد‬ ‫ﳏﻮر‬

13. 12
‫اﶈﻮر‬ ‫ﻳﺔ‬‫ر‬‫ﺑﺎﺧﺘﻴﺎ‬ ‫ﻳﺘﺼﻒ‬ ‫اﻟﺬي‬ ‫اﻟﻌﺮض‬ ‫ﺧﻂ‬ ‫ﳏﺪد‬ ‫أو‬ ‫اﻟﺜﺎﱐ‬ ‫اﳉﻴﻞ‬ ‫ﻣﻦ‬ ‫ﻛﻮ‬‫ﻓﻮ‬ ‫ﲜﺎﻳﺮوﺳﻜﻮب‬ ‫ﻳﺴﻤﻰ‬ ‫ﻣﺎ‬
.‫اﻟﻜﻮﱐ‬
.‫ﺑﻌﺪ‬ ‫ﻓﻴﻤﺎ‬ ‫ﻇﻬﺮت‬ ‫اﻟﱵ‬ ‫اﳌﺘﻘﺪﻣﺔ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫ﻟﻸﺟﻬﺰة‬ ‫ﻳﺔ‬‫ﺮ‬‫اﻟﻨﻈ‬ ‫اﻷﺳﺲ‬ ‫اﻷﺟﻬﺰة‬ ‫ﻫﺬﻩ‬ ‫ﲤﺜﻞ‬

14. 13
‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫اﻟﻄﺒﻴﻌﻲ‬‫اﻟﻄﺒﻴﻌﻲ‬
‫ﺿﺨﻢ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﻟﻮﻟﺐ‬ ‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬ ‫ﻫﻲ‬ ‫اﻟﱵ‬ (‫ﻛﺐ‬‫ﻛﻮ‬‫ﻛﻞ‬‫ﻋﺎم‬ ‫)وﺑﺸﻜﻞ‬ ‫اﻷرض‬ ،‫اﻟﻄﺒﻴﻌﻲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻋﻠﻰ‬ ‫اﻷﻣﺜﻠﺔ‬ ‫أﺷﻬﺮ‬ ‫ﻣﻦ‬
‫اﻟﻌﺎﱂ‬ ‫ﳏﻮر‬ ‫ﺣﻮل‬ ‫اﻧﻪ‬‫ر‬‫دو‬ ‫ﺑﻨﺘﻴﺠﺔ‬ ً‫ﺎ‬‫ﻧ‬‫ز‬‫ا‬‫ﻮ‬‫ﻣﺘ‬ ‫ﻳﺒﻘﻰ‬‫اﱄ‬‫ﻮ‬‫ﺣ‬ ‫اوﻳﺔ‬‫ﺰ‬‫ﺑ‬ ‫اﳌﺪاري‬ ‫اﳌﺴﺘﻮى‬ ‫ﻋﻠﻰ‬ ‫اﳌﺎﺋﻞ‬ ‫ﻟﻸرض‬ ‫اﻟﺬاﰐ‬ ‫)اﶈﻮر‬66.5
‫ﻗﺪرﻫﺎ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬ (‫درﺟﺔ‬15‫ﲢﺎﻓﻆ‬ ‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫وﻧﺘﻴﺠﺔ‬ .‫اﻟﻴﻮم‬ ‫ﰲ‬ ‫ﻛﺎﻣﻠﺔ‬‫دورة‬ ‫ﻳﻌﺎدل‬ ‫ﻣﺎ‬ ‫أي‬ ‫اﻟﺴﺎﻋﺔ‬ ‫ﰲ‬ ‫درﺟﺔ‬
) ٍ‫ز‬‫ا‬‫ﻮ‬‫ﻣﺘ‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫اﻷرض‬‫ﻟﻨﻔﺴﻪ‬ ً‫ﺎ‬‫ﻳ‬‫ز‬‫ا‬‫ﻮ‬‫ﻣ‬(‫ﻛﺘﻬﺎ‬‫ﺣﺮ‬ ‫رﻏﻢ‬ ‫اﻟﺬاﰐ‬ ‫ﶈﻮرﻫﺎ‬‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬ ‫ﻛﻤﺎ‬‫اﻟﺸﻤﺲ‬ ‫ﺣﻮل‬)7(‫ﻳﺒﻘﻰ‬ ‫ﺣﻴﺚ‬ ،
.(‫اﻟﻘﻄﱯ‬ ‫)اﻟﻨﺠﻢ‬ ‫اﻟﺒﻌﻴﺪة‬ ‫اﻟﻨﺠﻮم‬ ‫أﺣﺪ‬ ‫ﳓﻮ‬ ً‫ﺎ‬‫وﻣﺘﺠﻬ‬ ‫ﻟﻨﻔﺴﻪ‬ ً‫ﺎ‬‫ﻳ‬‫ز‬‫ا‬‫ﻮ‬‫ﻣ‬ ‫اﻷرض‬ ‫ان‬‫ر‬‫دو‬ ‫ﳏﻮر‬‫ﻛﺘﻠﺔ‬‫ﻫﻲ‬ ‫اﻷرض‬ ‫ﻓﺈن‬ ‫اﻟﺸﻜﻞ‬ ‫ﻬﺑﺬا‬
ٍ‫ز‬‫ا‬‫ﻮ‬‫ﻣﺘ‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫ﲢﺎﻓﻆ‬ ‫ﺳﻮف‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ‫اﻟﺬاﰐ‬ ‫ﳏﻮرﻫﺎ‬ ‫ﺣﻮل‬ ‫وﺗﺪور‬ ‫اﻟﺜﻼث‬ ‫اﶈﺎور‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫ﲤﺘﻠﻚ‬ ‫ﻋﻄﺎﻟﻴﺔ‬
‫ﻗﺪرﻩ‬ ‫ﺑﺪور‬ ‫داﺋﺮة‬ ‫ﻋﻠﻰ‬ ‫ﳏﻮرﻫﺎ‬ ‫ﻳﺘﺄرﺟﺢ‬ ‫اﻗﻊ‬‫ﻮ‬‫اﻟ‬ ‫)ﰲ‬ ‫اﻟﻘﻄﱯ‬ ‫اﻟﻨﺠﻢ‬ ‫ﺑﺎﲡﺎﻩ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫اﻟﺬاﰐ‬ ‫ﶈﻮرﻫﺎ‬25800‫ﺳﻨﺔ‬
.(ً‫ﺎ‬‫ﺛﺎﺑﺘ‬ ‫اﻋﺘﺒﺎرﻩ‬ ‫ﳝﻜﻦ‬ ‫ﻣﻌﻘﻮل‬ ‫ﻳﺐ‬‫ﺮ‬‫ﺑﺘﻘ‬ ‫وﺑﺎﻟﺘﺎﱄ‬
‫ﺣﻮل‬ ‫ج‬‫ﺗﺘﺪﺣﺮ‬ ‫ﺿﺨﻤﺔ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮﺑﻴﺔ‬ ‫اﻟﺐ‬‫ﻮ‬‫ﻟ‬ ‫ﻫﻲ‬ (.....‫اﳌﺸﱰي‬ ،‫)اﻷرض‬ ‫اﻛﺐ‬‫ﻮ‬‫اﻟﻜ‬‫و‬ (‫)اﻟﺸﻤﺲ‬ ‫اﻟﻨﺠﻮم‬ ‫أن‬ ‫ﻛﻤﺎ‬
ً‫ا‬‫ﺟﺪ‬ ‫اﻟﺒﻌﻴﺪة‬ ‫اﻟﻨﺠﻮم‬ ‫أو‬ ‫اﻟﻘﻄﱯ‬ ‫ﻟﻠﻨﺠﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻛﻴﺔ‬‫اﳊﺮ‬ ‫ﻋﺰوﻣﻬﺎ‬ ‫ﳏﺎور‬ ‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫ﲢﺎﻓﻆ‬ ‫وﻟﻜﻨﻬﺎ‬ ‫ﻧﻔﺴﻬﺎ‬.
‫اﻟﺸﻜﻞ‬5:‫اﳉﺎﻳﺮو‬‫اﻟﻄﺒﻴﻌﻲ‬

15. 14
‫دراﺳﺔ‬‫دراﺳﺔ‬‫اﻟﺠﺎﻳﺮ‬ ‫ﺣﺮﻛﺔ‬‫اﻟﺠﺎﻳﺮ‬ ‫ﺣﺮﻛﺔ‬‫اﻟﺤﺮﻳﺔ‬ ‫درﺟﺎت‬ ‫ﺛﻼﺛﻲ‬ ‫و‬‫اﻟﺤﺮﻳﺔ‬ ‫درﺟﺎت‬ ‫ﺛﻼﺛﻲ‬ ‫و‬‫وﺧﻮاﺻﻪ‬‫وﺧﻮاﺻﻪ‬
(‫اﻧﻴﺔ‬‫ر‬‫دو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺎت‬ ‫ﺛﻼث‬ ‫ﳝﺘﻠﻚ‬ ‫)أي‬ ‫وﺣﻴﺪة‬ ‫ﺗﻜﺎز‬‫ر‬‫ا‬ ‫ﻧﻘﻄﺔ‬ ‫اﱃ‬ ‫وﻳﺴﺘﻨﺪ‬ ‫ﻋﺎﻟﻴﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻳﺪور‬ ‫ﺻﻠﺐ‬ ‫ﺟﺴﻢ‬ ‫ﻛﻞ‬‫أن‬ ‫ﺗﺒﲔ‬
.‫ﺧﺎرﺟﻴﺔ‬ ‫ﻋﺰوم‬ ‫ﻋﻠﻴﻪ‬ ‫ﺗﺆﺛﺮ‬ ‫ﱂ‬ ‫إذا‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫ﺛﺎﺑﺘﺎ‬ ‫ﻧﻪ‬‫ر‬‫ا‬‫و‬‫د‬ ‫ﳏﻮر‬ ‫ﻋﻠﻰ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬
.ً‫ﺎ‬‫ﺟﺎﻳﺮوﺳﻜﻮﺑﻴ‬ ً‫ﺎ‬‫ﺟﺴﻤ‬ ‫ﻋﻨﺪﻫﺎ‬ ‫اﳋﺎﺻﻴﺔ‬ ‫ﻫﺬﻩ‬ ‫ﳝﺘﻠﻚ‬ ‫اﻟﺬي‬ ‫اﳉﺴﻢ‬ ‫وﻳﺴﻤﻰ‬
) ‫اﻟﺸﻜﻞ‬ ‫ﰲ‬ ‫اﳌﺒﲔ‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻻﺳﺘﻨﺎد‬ ‫إﻃﺎر‬ ‫ذو‬ ‫اﳌﻴﻜﺎﻧﻴﻜﻲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻳﻌﺘﱪ‬8‫ﻳﺔ‬‫ﺮ‬‫ﻟﻨﻈ‬ ‫اﻟﻔﻌﻠﻲ‬ ‫اﻟﺘﺤﻘﻴﻖ‬ ‫ﻃﺮق‬ ‫أﻗﺪم‬‫و‬ ‫أﺑﺴﻂ‬ ‫ﻣﻦ‬ (
.‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﳉﺴﻢ‬‫و‬ ‫اﳉﺎﻳﺮو‬
H
Пл
X
Y
Z
My
Xω
DYx
DMx
DYy
DMy
H
‫اﻟﺸﻜﻞ‬6‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ :

16. 15
‫ﺟﺴﻢ‬ ‫ﲟﺜﺎﺑﺔ‬ ‫اﶈﺮك‬ ‫ار‬‫و‬‫د‬ ‫ﻟﻴﺼﺒﺢ‬ ‫ﺑﺎﺋﻲ‬‫ﺮ‬‫ﻛﻬ‬‫ﳏﺮك‬ ‫اﺳﺘﺨﺪام‬ ‫ﻳﺘﻢ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﺟﺴﻢ‬ ‫ﻋﻠﻰ‬ ‫اﳊﺼﻮل‬ ‫وﻬﺑﺪف‬ ‫أﻧﻪ‬ ‫إذ‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫ﳝﺘﻠﻚ‬ ‫أﻧﻪ‬ ‫ﺣﻴﺚ‬ ‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬( )Z‫إﻃﺎر‬ ‫ﻣﻊ‬ ‫ار‬‫و‬‫اﻟﺪ‬ ‫ﳝﻠﻚ‬ ‫وﺣﻴﺚ‬ ‫اﶈﺮك‬ ‫ﳉﺴﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫اﺳﺘﻨﺎدﳘﺎ‬ ‫ﻳﺘﻢ‬ ‫اﻟﺪاﺧﻠﻲ‬ ‫اﻻﺳﺘﻨﺎد‬( )X‫إﻃﺎر‬ ‫ﳝﻠﻚ‬ . ‫ﺧﺎرﺟﻲ‬ ‫اﻻﺳﺘﻨﺎد‬ ‫ﻹﻃﺎر‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ (‫اﻟﺪاﺧﻠﻲ‬ ‫اﻻﺳﺘﻨﺎد‬ ‫وإﻃﺎر‬ ‫ار‬‫و‬‫اﻟﺪ‬ ‫)وﻣﻌﻪ‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻻﺳﺘﻨﺎد‬( )Y.‫ﻛﻜﻞ‬‫اﳉﻬﺎز‬ ‫ﳉﺴﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬
‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻟﺴﺮﻋﺔ‬ ‫ﺑﺎﻹﺿﺎﻓﺔ‬ ‫ﳝﺘﻠﻚ‬ ‫ﻛﻮﻧﻪ‬ً‫ﺎ‬‫ﺟﺎﻳﺮوﺳﻜﻮﺑﻴ‬ ً‫ﺎ‬‫ﺟﺴﻤ‬ ‫ﻋﺎﻟﻴﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺪوﻳﺮﻩ‬ ‫ﺣﺎل‬ ‫ﰲ‬ ‫اﶈﺮك‬ ‫ار‬‫و‬‫د‬ ‫ﻳﺼﺒﺢ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻬﺑﺬا‬
‫اﶈﺎور‬ ‫ﺣﻮل‬ ‫اﻧﻴﺔ‬‫ر‬‫دو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺎت‬ ‫ﺛﻼث‬ ‫اﻟﻌﺎﻟﻴﺔ‬( , , )X Y Z‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﻋﻠﻰ‬ ‫ﻓﻴﺤﺎﻓﻆ‬( )H‫ﰲ‬ ‫ﺛﺎﺑﺘﺎ‬
.‫ﺧﺎﺟﻴﺔ‬ ‫ﻋﺰوم‬ ‫ﻋﻠﻴﻪ‬ ‫ﺗﺆﺛﺮ‬ ‫ﱂ‬ ‫إذا‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬
‫ﻳﻦ‬‫ر‬‫اﶈﻮ‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫ﺑﺎﻟﺪو‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﺗﺴﻤﺢ‬ ‫اﻟﱵ‬‫و‬ ‫اﳋﺎرﺟﻲ‬‫و‬ ‫اﻟﺪاﺧﻠﻲ‬ ‫اﻹﺳﺘﻨﺎدﻳﻦ‬ ‫ﻣﻦ‬ ‫اﳌﺆﻟﻔﺔ‬ ‫اﻟﻮﺻﻠﺔ‬ ‫ﺗﺴﻤﻰ‬( , )X Y‫ﺑﻮﺻﻠﺔ‬
‫اﶈﻮر‬ ‫وﻳﺴﻤﻰ‬ "‫"ﻛﺎردان‬( )Z‫ان‬‫ر‬‫اﶈﻮ‬ ‫ﻳﺴﻤﻰ‬ ‫ﺑﻴﻨﻤﺎ‬ ،‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﲟﺤﻮر‬( , )X Y‫ﺣﺴﺎﺳﻴﺔ‬ ‫ﲟﺤﻮري‬
.‫اﻟﻌﺰوم‬ ‫ﻫﺬﻩ‬ ‫ﺑﺘﺄﺛﲑ‬ ‫اﲡﺎﻫﻪ‬ ‫وﻳﻐﲑ‬ ‫ﻳﻦ‬‫ر‬‫اﶈﻮ‬ ‫ﻫﺬﻳﻦ‬ ‫ﻋﻠﻰ‬ ‫اﳌﻄﺒﻘﺔ‬ ‫ﻟﻠﻌﺰوم‬ ‫ﻳﺘﺤﺴﺲ‬ ‫اﳉﺎﻳﺮو‬ ‫أن‬ ‫إذ‬ ‫اﳉﺎﻳﺮو‬
‫اوﻳﺔ‬‫ز‬ ‫ﲝﺴﺎﺳﺎت‬ ‫اﳊﺴﺎﺳﻴﺔ‬ ‫ﳏﻮري‬ ‫ﺗﺰوﻳﺪ‬ ‫ﻳﺘﻢ‬ ‫اﳉﺎﻳﺮو‬ ‫اص‬‫ﻮ‬‫ﺧ‬ ‫ﻣﻦ‬ ‫ﻟﻼﺳﺘﻔﺎدة‬( , )DYx DYy‫ان‬‫ر‬‫دو‬ ‫اﻳﺎ‬‫و‬‫ز‬ ‫ﻟﺘﺤﺴﺲ‬
‫اﻟﻌﺰوم‬ ‫ﻣﻮﻟﺪات‬ ‫ﺗﺴﺘﺨﺪم‬ ‫ﻛﻤﺎ‬‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﳋﺎرﺟﻲ‬‫و‬ ‫اﻟﺪاﺧﻠﻲ‬ ‫ﻳﻦ‬‫ر‬‫اﻹﻃﺎ‬( , )DMx DMy‫ﺗﺪوﻳﺮﻩ‬ ‫أي‬ ‫اﳉﺎﻳﺮو‬ ‫ﻟﺘﻮﺟﻴﻪ‬
‫اﶈﺎور‬ ‫ﺣﻮل‬( , )X Y.‫اﻟﺬاﰐ‬ ‫ﳏﻮرﻩ‬ ‫ﲟﻨﺤﻰ‬ ‫اﻟﺘﺤﻜﻢ‬ ‫أي‬
‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﳌﺒﲔ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ ‫اﺳﺘﺨﺪام‬ ‫ﺳﻴﺘﻢ‬8‫ﻫﺬﻩ‬ ‫اﻟﺪرﺳﺔ‬ ‫أن‬ ً‫ﺎ‬‫ﻋﻠﻤ‬ ،‫اﺻﻪ‬‫ﻮ‬‫ﺧ‬ ‫اﺳﺔ‬‫ر‬‫ودد‬ ‫اﳉﺎﻳﺮو‬ ‫ﻣﻌﺎدﻻت‬ ‫ﻻﺷﺘﻘﺎق‬
.‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﺟﺴﻢ‬ ‫ﻷي‬ ‫اﻷﺳﺎﺳﻴﺔ‬ ‫اص‬‫ﻮ‬‫اﳋ‬‫و‬ ‫اﻟﻨﺘﺎﺋﺞ‬ ‫ﻧﺎﺣﻴﺔ‬ ‫ﻣﻦ‬ ‫ﺻﺤﻴﺤﺔ‬ ‫ﺗﺒﻘﻰ‬
‫ﻣﻌﺎدﻻت‬‫ﻣﻌﺎدﻻت‬‫اﻟﺤﺮﻛﺔ‬‫اﻟﺤﺮﻛﺔ‬
1.‫ﻛﺔ‬‫اﻟﺤﺮ‬ ‫ﻣﻌﺎدﻻت‬‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ﻓﻲ‬:
‫أوﻳﻠﺮ‬ ‫ﻣﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﻣﻌﺎدﻻت‬ ‫ﻻﺷﺘﻘﺎق‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﳝﻜﻦ‬Euler‫ﻣﻌﺎدﻻت‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫أو‬ ،‫اﻟﺪﻳﻨﺎﻣﻴﻜﻴﺔ‬
‫ﻛﺔ‬‫ﻟﻠﺤﺮ‬ ‫اﻧﺞ‬‫ﺮ‬‫ﻻﻏ‬Lagrange's equations of motion‫اﻟﺘﺤﻮﻳﻼت‬ ‫اء‬‫ﺮ‬‫وﺑﺈﺟ‬ ،‫داﳌﺒﲑ‬ ‫ﻣﺒﺪأ‬ ‫ﺑﺘﻄﺒﻴﻖ‬ ‫أو‬
:‫اﳉﺎﻳﺮو‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﳌﻌﺎدﻻت‬ ‫اﳌﺒﺴﻂ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻋﻠﻰ‬ ‫اﳊﺼﻮل‬ ‫ﳝﻜﻦ‬ ‫اﻟﺒﺴﻴﻄﺔ‬

17. 16
X X Z Y X
Y Y Z X Y
I H M
I H M
θ θ
θ θ
 ⋅ + ⋅ = 
 ⋅ − ⋅ = 
 
 
(1.1)
:‫ﺣﻴﺚ‬
,X YI‫ال‬ ‫ﻋﺰوم‬‫ﻋﻄﺎﻟﺔ‬‫ﻟﻠﺠﺴﻢ‬.‫اﻷﺳﺎﺳﻴﺔ‬ ‫ﳏﺎورﻩ‬ ‫ﺣﻮل‬
,X Yθ‫ﺷﻌﺎع‬‫ال‬‫ﺳﺮﻋﺔ‬‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬‫ل‬‫ﺣﻮل‬ ‫ﳉﺴﻢ‬‫اﳌﺢ‬‫اﻷﺳﺎﺳﻴﺔ‬ ‫اور‬.
,X Yθ‫ﺷﻌﺎع‬‫ع‬‫اﻟﺘﺴﺎر‬‫اوي‬‫ﺰ‬‫اﻟ‬‫ل‬‫ﺣﻮل‬ ‫ﳉﺴﻢ‬‫اﳌﺢ‬‫اﻷﺳﺎﺳﻴﺔ‬ ‫اور‬.
,X YM‫اﳌﺆﺛﺮة‬ ‫اﳋﺎرﺟﻴﺔ‬ ‫اﻟﻌﺰوم‬‫ﺣﻮل‬‫اﳌﺢ‬‫اﻷﺳﺎﺳﻴﺔ‬ ‫اور‬.
‫اﳉﺎﻳﺮو‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﺗﺼﻒ‬ ‫اﻟﱵ‬ ‫اﻟﺘﻔﺎﺿﻠﻴﺔ‬ ‫اﳌﻌﺎدﻻت‬ ‫ﲨﻠﺔ‬ ‫وﻫﻲ‬‫اﻟﺜﺎﱐ‬ ‫اﳊﺪ‬ ‫ﳝﺜﻞ‬ ‫وﻓﻴﻬﺎ‬[]‫اﳌﻌﺎدﻟﺘﲔ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬‫ﻣﻦ‬(1.1)
.‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﻛﺒﱵ‬‫ﻣﺮ‬ ‫إﺣﺪى‬
‫ﻓﺎرق‬ ‫ﻣﻊ‬ ،‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﻛﺔ‬‫ﳊﺮ‬ ‫اﻷﺳﺎﺳﻲ‬ ‫اﻟﻘﺎﻧﻮن‬ ‫ﻣﻊ‬ ‫ﻳﺘﺸﺎﺑﻪ‬ ‫اﳌﻌﺎدﻻت‬ ‫ﺷﻜﻞ‬ ‫أن‬ ‫اﺿﺢ‬‫ﻮ‬‫اﻟ‬ ‫ﻣﻦ‬‫ﻇﻬﻮر‬ ‫وﻫﻮ‬ ‫أﺳﺎﺳﻲ‬
‫اﳉﺴﻢ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫وﺑﲔ‬ ،‫اﻟﺘﻘﻠﻴﺪي‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﺑﲔ‬ ‫اﻷﺳﺎﺳﻲ‬ ‫اﻟﻔﺮق‬ ‫ﻫﻮ‬ ‫اﳊﺪ‬ ‫وﻫﺬا‬ .‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﻟﻠﻌﺰم‬ ‫ﱢﻞ‬‫ﺜ‬‫اﳌﻤ‬ ‫اﳊﺪ‬
.‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﺼﻠﺐ‬
.‫ﺋﻴﺴﺔ‬‫ﺮ‬‫اﻟ‬ ‫ﻳﺎﺋﻴﺔ‬‫ﺰ‬‫اﻟﻔﻴ‬ ‫اﺻﻪ‬‫ﻮ‬‫ﳋ‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﳝﻜﻦ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﳌﺒﺴﻂ‬ ‫ﻳﺎﺿﻲ‬‫ﺮ‬‫اﻟ‬ ‫اﻟﻨﻤﻮذج‬ ‫اﺳﺔ‬‫ر‬‫د‬ ‫ﻣﻦ‬
2.‫اﻟﺬاﺗﻴﺔ‬ ‫ﻛﺔ‬‫اﻟﺤﺮ‬‫ل‬‫ﻟﺞ‬‫ا‬:‫ﻳﺮو‬
.‫ﺧﺎرﺟﻲ‬ ‫ﻋﺰم‬ ‫ﺗﺄﺛﲑ‬ ‫ﺑﺪون‬ ‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻫﻲ‬ ‫اﻟﺬاﺗﻴﺔ‬ ‫ﻛﺔ‬‫اﳊﺮ‬‫ﻟﺬﻟﻚ‬‫اﳌﻌﺎدﻟﺘﲔ‬ ‫ﰲ‬ ‫ﺑﺎﻟﺼﻔﺮ‬ ‫اﳋﺎرﺟﻴﺔ‬ ‫اﻟﻌﺰوم‬ ‫ﻗﻴﻢ‬ ‫ﺑﺘﻌﻮﻳﺾ‬
(1.1):‫ﳒﺪ‬
Z
X Y
X
Z
Y X
Y
H
I
H
I
θ θ
θ θ
=− ⋅
= ⋅
 
 
(1.2)
‫اﳌﻌﺎدﻟﺔ‬ ‫ﻣﻦ‬(1.2):‫ﳒﺪ‬
Z
Y X
Y
H
A
I
θ θ= ⋅ + (1.3)
‫اﳌﻌﺎدﻟﺔ‬ ‫ض‬‫ﱢ‬‫ﻮ‬‫ﻧﻌ‬(1.3)‫اﳌﻌﺎدﻟﺔ‬ ‫ﰲ‬(1.2):‫ﳒﺪ‬

18. 17
0
2
=+⋅+ A
I
H
II
H
X
Z
X
YX
Z
X θθ
:‫ﳒﺪ‬ ‫ﺑﺎﳊﻞ‬
Z
Y
YX
Z
X
H
AI
t
II
H
CosB
⋅
−








+⋅= ϕθ
:‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻻﺑﺘﺪاﺋﻴﺔ‬ ‫اﻟﺸﺮوط‬ ‫ﻧﻀﻊ‬ ‫اﺑﺖ‬‫ﻮ‬‫اﻟﺜ‬ ‫ﻟﺘﺤﺪﻳﺪ‬
( )
( ) 


==
==
00
00
t
t
X
X
θ
θ

:‫ﳒﺪ‬
Z
Y
Z
Y
H
AI
B
H
AI
B
Sin
⋅
=⇒=
⋅
−
=⇒=
0
00 ϕϕ
‫ﻋﺒﺎرة‬ ‫ﻟﺘﺼﺒﺢ‬Xθ:‫اﻟﺸﻜﻞ‬ ‫ﻣﻦ‬
0
1Y Z
X X
Z X Y
I H
Cos t
H I I
θ θ
  
 =⋅ − 
   
 (1.4)
‫اﳌﻌﺎدﻟﺔ‬ ‫ﻣﻦ‬(1.2):‫ﳒﺪ‬
. Z
Y
X Y
H
A Cos t
I I
θ
 
=   
 

:‫ﳒﺪ‬ ‫ﺑﺎﳊﻞ‬
Ct
II
H
SinA
H
II
YX
Z
Z
YX
Y +








⋅⋅=θ
‫اﻻﺑﺘﺪاﺋﻲ‬ ‫اﻟﺸﺮط‬ ‫ﻣﻦ‬( ) 00 ==tYθ‫أن‬ ‫ﳒﺪ‬0=C‫ﻋﺒﺎرة‬ ‫ﻟﺘﺼﺒﺢ‬Yθ:‫اﻟﺸﻜﻞ‬ ‫ﻣﻦ‬
X Y Z
Y
Z X Y
I I H
A Sin t
H I I
θ
 
= ⋅ ⋅  
 
(1.5)

19. 18
‫أن‬ ‫ﺑﻔﺮض‬YX III ==‫اﻟﱰﻧﺢ‬ ‫ﺗﺮدد‬ ‫ف‬‫ﱢ‬‫ﺮ‬‫ﻧﻌ‬ ،Z
ZZ
I
I
I
H
n θ==‫اﳌﻌﺎدﻟﺘﺎن‬ ‫ﻓﺘﺼﺒﺢ‬(1.4)‫و‬(1.5)
:‫اﻟﺘﺎﱄ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻋﻠﻰ‬
( )
( )
0
0
1
Y
X
Y
Y
C
Cos nt
n
C
Sin nt
n
θ
θ
= −  
=
(1.6)
‫ﻟﻠﺠﺎﻳﺮو،ﺣﻴﺚ‬ ‫اﳊﺮة‬ ‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻣﻌﺎدﻻت‬ ‫وﻫﻲ‬‫اﶈﻮر‬ ‫وﻓﻖ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻳﺎدة‬‫ﺰ‬‫ﺑ‬ ‫أﻧﻪ‬ ‫ﻧﻼﺣﻆ‬Z( )Zθ‫اﻟﱰﻧﺢ‬ ‫ﺗﺮدد‬ ‫ﻗﻴﻤﺔ‬ ‫ﺗﺰداد‬
n‫اوﻳﺘﲔ‬‫ﺰ‬‫اﻟ‬ ‫ﻛﻼ‬‫ﻣﻄﺎل‬ ‫ﻳﺼﻐﺮ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ،Xθ‫و‬Yθ‫اﻟﺬاﰐ‬ ‫اﻧﻪ‬‫ر‬‫دو‬ ‫ﳏﻮر‬ ‫اﳉﺎﻳﺮوﺣﻮل‬ ‫ان‬‫ر‬‫دو‬ ‫ﺳﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ .
‫أﺣﺪ‬ ‫ﺣﻮل‬ ‫ﻣﺎ‬ ‫ﺟﺴﻢ‬ ‫ان‬‫ر‬‫دو‬ ‫ﺣﺎل‬ ‫ﰲ‬ ‫أﻧﻪ‬ ‫ﲟﻌﲎ‬ .‫ﻣﻌﺪوم‬ ‫ﺷﺒﻪ‬ ‫ﻳﻦ‬‫ﺮ‬‫اﻵﺧ‬ ‫ﻳﻦ‬‫ر‬‫اﶈﻮ‬ ‫ﺣﻮل‬ ‫ازﻩ‬‫ﺰ‬‫اﻫﺘ‬ ‫ﻳﻜﻮن‬ ٍ‫ﻛﺎف‬‫ﺑﺸﻜﻞ‬ ‫ﻛﺒﲑة‬
‫ﻫﺬا‬ ‫ﻓﺈن‬ ‫ﺧﺎرﺟﻴﺔ‬ ‫ﻟﻌﺰوم‬ ‫ﺗﻌﺮﺿﻪ‬ ‫ﻋﺪم‬ ‫وﻣﻊ‬ ‫ﻳﻦ‬‫ﺮ‬‫اﻵﺧ‬ ‫ﻳﻪ‬‫ر‬‫ﳏﻮ‬ ‫ﺣﻮل‬ ‫اﻧﻪ‬‫ر‬‫دو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫ﻣﻊ‬ ‫ﻛﺒﲑة‬‫ان‬‫ر‬‫دو‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻷﺳﺎﺳﻴﺔ‬ ‫ﳏﺎورﻩ‬
.‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﺳﺮﻋﺔ‬ ‫ازدادت‬ ‫ﻛﻠﻤﺎ‬‫ﻳﺼﻐﺮ‬ ‫ﲞﻄﺄ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫ﺛﺎﺑﺖ‬ ‫اﲡﺎﻩ‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬ ‫اﳉﺴﻢ‬
‫ﻧﺴﺘﻨﺘﺞ‬ ‫وﺑﺬﻟﻚ‬‫اﻷوﻟﻰ‬ ‫اﻟﺨﺎﺻﺔ‬‫أن‬ ‫وﻫﻲ‬ ‫ﻟﻠﺠﺎﻳﺮوﺳﻜﻮب‬‫اﻟﺠﺎﻳﺮو‬ "‫ل‬ ‫اﻟﻤﺘﻌﺮض‬ ‫)ﻏﻴﺮ‬ ‫اﻟﺤﺮ‬‫ﺧﺎرﺟﻴﺔ‬ ‫ﻟﻌﺰوم‬(
".‫اﻟﻌﻄﺎﻟﻲ‬ ‫ﻟﻠﻔﻀﺎء‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ً‫ﺎ‬‫ﺛﺎﺑﺘ‬ (‫ﻛﻲ‬‫اﻟﺤﺮ‬ ‫اﻟﻌﺰم‬ ‫)ﻣﺤﻮر‬ ‫اﻷﺳﺎﺳﻲ‬ ‫ﻣﺤﻮرﻩ‬ ‫اﺗﺠﺎﻩ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺎﻓﻆ‬‫اﻻﻫﺘﺰاز‬ ‫إﻫﻤﺎل‬ ‫ﻣﻊ‬
.!‫ﺟﺪا‬ ‫ﻋﺎﻟﻲ‬ ‫وﺗﺮدد‬ ً‫ا‬‫ﺟﺪ‬ ‫ﺻﻐﻴﺮ‬ ‫ﺑﻤﻄﺎل‬
‫ا‬‫ا‬‫ﻻ‬‫ﻻ‬‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻟﺬاﺗﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫أن‬ ‫اﺳﺘﻨﺘﺎﺟﻪ‬ ‫ﳝﻜﻦ‬ ‫اﻟﺬي‬ ‫اﻟﺜﺎﻧﻮي‬ ‫ﺳﺘﻨﺘﺎج‬‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻟﺬاﺗﻴﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫أن‬ ‫اﺳﺘﻨﺘﺎﺟﻪ‬ ‫ﳝﻜﻦ‬ ‫اﻟﺬي‬ ‫اﻟﺜﺎﻧﻮي‬ ‫ﺳﺘﻨﺘﺎج‬( )Zθ‫ﻋﻠﻰ‬ ‫ﺗﺆﺛﺮ‬ ‫ﻻ‬ ‫ﻛﺎﻧﺖ‬‫وإن‬
‫اﻟﺬاﺗﻴﺔ‬ ‫ﺑﺎﻟﺴﺮﻋﺔ‬ ‫ﻣﺘﻌﻠﻘﺔ‬ ‫ﻏﲑ‬ ‫ﻛﺎﻧﺖ‬‫وإن‬ ‫ﻳﺎﺋﻴﺔ‬‫ﺰ‬‫اﻟﻔﻴ‬ ‫اﳉﺎﻳﺮو‬ ‫اص‬‫ﻮ‬‫ﺧ‬ ‫أن‬ ‫ﻳﻌﲏ‬ ‫ﲟﺎ‬ .‫دﻗﺘﻪ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺆﺛﺮ‬ ‫ﻓﺈ�ﺎ‬ ‫ﺋﻴﺴﻴﺔ‬‫ﺮ‬‫اﻟ‬ ‫اﺻﻪ‬‫ﻮ‬‫ﺧ‬
.‫اﻟﺘﻘﻨﻴﺔ‬ ‫اﺻﻪ‬‫ﻮ‬‫ﺧ‬ ‫ﻋﻠﻰ‬ ‫أي‬ ‫دﻗﺘﻪ‬ ‫اﺻﻔﺎت‬‫ﻮ‬‫ﻣ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺆﺛﺮ‬ ‫ﻓﺈ�ﺎ‬ ،‫ﻟﻠﺠﺎﻳﺮو‬
3.‫ا‬:‫ﻟﻠﺠﺎﻳﺮوﺳﻜﻮب‬ ‫ﻳﺔ‬‫ﺮ‬‫اﻟﻘﺴ‬ ‫ﻛﺔ‬‫ﻟﺤﺮ‬
‫اﳌﻌﺎدﻟﺘﲔ‬ ‫ﲨﻠﺔ‬ ‫إﱃ‬ ‫ﺑﺎﻟﻌﻮدة‬(1.1)‫)ﻣﻊ‬ ‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﺑﺎﺷﺘﻘﺎق‬ ‫ﳒﺪ‬‫اض‬‫ﱰ‬‫اﻓ‬‫اﳌﻄﺒﻖ‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫أن‬YM
:‫اﻷوﱃ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﰲ‬ ‫اﻟﺘﺒﺪﻳﻞ‬‫و‬ (‫ﺛﺎﺑﺖ‬
XYZY
Z
YX
MH
H
II
=⋅+⋅ θθ 
‫ﻧﻀﻊ‬YX θ=:‫ﳒﺪ‬

20. 19
Bt
H
M
t
II
H
Sin
H
IIA
H
M
t
II
H
CosAXM
II
H
X
II
H
X
Z
X
YX
Z
Z
YX
Y
Z
X
YX
Z
YX
YX
Z
YX
Z
+⋅+








+⋅⋅
⋅
=⇒
+








+⋅⋅==⇒⋅=⋅+
ϕθ
ϕθ
2
‫ﻋﻠﻰ‬ ‫ﳓﺼﻞ‬ ‫ﲝﻴﺚ‬ ‫اﻟﺰﻣﻦ‬ ‫ﻣﺒﺪأ‬ ‫اﺧﱰﻧﺎ‬ ‫أﻧﻨﺎ‬ ‫وﺑﻔﺮض‬0=ϕ:‫اﻟﺘﺎﱄ‬ ‫اﻟﻨﺤﻮ‬ ‫ﻋﻠﻰ‬ ‫ﻓﺔ‬‫ﱠ‬‫ﺮ‬‫ﻣﻌ‬ ‫اﻻﺑﺘﺪاﺋﻴﺔ‬ ‫اﻟﺸﺮوط‬ ‫أن‬‫و‬ ،
( )
( ) 


==
==
00
00
t
t
Y
X
θ
θ
:‫ﳒﺪ‬




−=
=
Z
X
H
M
A
B 0
:‫ﻋﻠﻰ‬ ‫ﳓﺼﻞ‬ ‫وﺑﺎﻟﺘﺎﱄ‬















 ⋅
⋅−=
YX
Z
YX
Z
X
Y
II
tH
SinIIt
H
M
θ
‫اﳌﻌﺎدﻟﺘﲔ‬ ‫ﲨﻠﺔ‬ ‫إﱃ‬ ‫ﺑﺎﻟﻌﻮدة‬(1.1):‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﻣﻦ‬ ‫ﳒﺪ‬
Y
Z
Y
Z
Y
X
H
I
H
M
θθ  ⋅+−=








⋅
⋅
= t
II
H
Sin
II
HM
YX
Z
YX
ZX
Yθ
C
II
tH
Cos
H
I
Mt
H
M
II
tH
Sin
I
I
M
H
M
YX
Z
Z
Y
X
Z
Y
X
YX
Z
X
Y
X
Z
Y
X
+







 ⋅
⋅⋅−⋅−=⇒







 ⋅
⋅⋅+−=⇒
θ
θ
‫ﳒﺪ‬ ‫اﻻﺑﺘﺪاﺋﻴﺔ‬ ‫اﻟﺸﺮوط‬ ‫وﻣﻦ‬
Z
YX
H
IM
C
⋅
=
:‫ﻳﻠﻲ‬ ‫ﻛﻤﺎ‬‫اﻟﻨﻬﺎﺋﻴﺔ‬ ‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻣﻌﺎدﻻت‬ ‫ﺗﻜﻮن‬ ‫ﺑﺎﻟﺘﺎﱄ‬

21. 20
1Y X Y Z
X
Z Z X Y
X Z
Y X Y
Z X Y
M M I H t
t Cos
H H I I
M H t
t I I Sin
H I I
θ
θ
  ⋅ ⋅
=− ⋅ − ⋅ −  
    
  ⋅
= − ⋅  
    
(1.7)
‫و‬ ‫ﻳﺔ‬‫ﺮ‬‫اﻟﻘﺴ‬ ‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻋﻦ‬ ‫اﳌﻌﱪة‬ ‫اﳌﻌﺎدﻻت‬ ‫ﲨﻠﺔ‬ ‫وﻫﻲ‬‫ﻳﺔ‬‫ز‬‫ا‬‫ﺰ‬‫اﻻﻫﺘ‬ َ‫ﺔ‬‫ﻛ‬‫اﳊﺮ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻛﻞ‬‫ﻣﻦ‬ ‫اﻟﺜﺎﱐ‬ ‫اﻟﻄﺮف‬ ‫ﻣﻦ‬ ‫اﻟﺜﺎﱐ‬ ‫ﱡ‬‫ﺪ‬‫اﳊ‬ ‫ﳝﺜﻞ‬
،‫ﻟﻠﺠﺎﻳﺮوﺳﻜﻮب‬‫ﺑﻴﻨﻤﺎ‬‫اﳉﺎﻳﺮو‬ ‫اﺳﺘﺠﺎﺑﺔ‬ ‫اﻷول‬ ‫اﳊﺪ‬ ‫ﳝﺜﻞ‬‫ﻛﺔ‬‫ﻟﻠﺤﺮ‬ ‫اﳌﻤﺜﻠﲔ‬ ‫اﳊﺪﻳﻦ‬ ‫ﺑﺈﳘﺎل‬ ‫ﺑﺎﻟﺘﺎﱄ‬ .‫اﳌﻄﺒﻖ‬ ‫اﳋﺎرﺟﻲ‬ ‫ﻟﻠﻌﺰم‬
‫أن‬ ‫ﺣﻴﺚ‬ ‫ﻳﻦ‬‫ﺮ‬‫اﻵﺧ‬ ‫اﳊﺪﻳﻦ‬ ‫أﻣﺎم‬ ‫ﻟﺼﻐﺮﳘﺎ‬ ‫ﻳﺔ‬‫ز‬‫ا‬‫ﺰ‬‫اﻻﻫﺘ‬YXZYZ IIHIH >>>> ,:‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻋﻠﻰ‬ ‫ﳓﺼﻞ‬
Y
X
Z
X
Y
Z
M
t
H
M
t
H
θ
θ
=− ⋅
=
(1.8)
‫اﶈﻮر‬ ‫ﺣﻮل‬ ٍ‫ﻋﺰم‬ ‫ﺗﻄﺒﻴﻖ‬ ‫أن‬ ‫ﻣﻼﺣﻈﺔ‬ ‫ﳝﻜﻦ‬ ‫اﻟﺴﺎﺑﻘﺘﲔ‬ ‫اﻟﻌﻼﻗﺘﲔ‬ ‫ﻣﻦ‬X‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫دو‬ ‫إﱃ‬ ‫ﻳﺆدي‬Yٍ‫ﻋﺰم‬ ‫ﺗﻄﺒﻴﻖ‬ ‫أن‬‫و‬
‫اﶈﻮر‬ ‫ﺣﻮل‬Y‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ان‬‫ر‬‫دو‬ ‫إﱃ‬ ‫ﻳﺆدي‬X‫ﻧﺴﺘﻨﺘﺞ‬ ‫وﻣﻨﻪ‬ .:
‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺨﺎﺻﺔ‬:‫وﻫﻲ‬ ‫ﻟﻠﺠﺎﻳﺮوﺳﻜﻮب‬‫اﻟﺠﺎﻳﺮو‬ ‫ﺣﺴﺎﺳﻴﺔ‬ ‫ﻣﺤﺎور‬ ‫أﺣﺪ‬ ‫ﺣﻮل‬ ‫ﺧﺎرﺟﻲ‬ ‫ﻋﺰم‬ ‫ﺗﺄﺛﻴﺮ‬ ‫"ﻋﻨﺪ‬‫ﻓﺴﻮف‬
".‫اﻵﺧﺮ‬ ‫اﻟﺤﺴﺎﺳﻴﺔ‬ ‫ﻣﺤﻮر‬ ‫ﺣﻮل‬ ‫ﻳﺪور‬‫اﶈﺎور‬ ‫ﳘﺎ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺣﺴﺎﺳﻴﺔ‬ ‫ا‬‫ر‬‫)ﳏﻮ‬X‫و‬Y‫اﳌﻌﺎﻣﺪة‬‫و‬ ‫ﺑﻴﻨﻬﺎ‬ ‫ﻓﻴﻤﺎ‬ ‫اﳌﺘﻌﺎﻣﺪة‬
‫اﻟﺬاﰐ‬ ‫ﻟﻠﻤﺤﻮر‬Z‫اﻟﺸﻜﻞ‬ ‫ﰲ‬ ‫ﻛﻤﺎ‬‫ﻟﻠﺠﺎﻳﺮو‬7.(‫ال‬ ‫ﺗﺄﺛﲑ‬ ‫أن‬ ‫أي‬‫ﻋﺰم‬‫اﱁ‬‫اﳉﺎﻳﺮو‬ ‫ﺣﺴﺎﺳﻴﺔ‬ ‫ﳏﺎور‬ ‫أﺣﺪ‬ ‫ﺣﻮل‬ ‫ارﺟﻲ‬)X
(ً‫ﻼ‬‫ﻣﺜ‬‫ﻓﺴﻮف‬‫ﻟﻦ‬‫ﺣﻮل‬ ‫ﻳﺪور‬‫اﳌﺢ‬ ‫ﻧﻔﺲ‬‫ور‬‫ﳏﻮر‬ ‫ﺣﻮل‬ ‫ﺳﻴﺪور‬ ‫ﺑﻞ‬ ‫اﻟﺘﻘﻠﻴﺪي‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﰲ‬ ‫اﳊﺎل‬ ‫ﻫﻲ‬ ‫ﻛﻤﺎ‬‫اﳊﺴﺎﺳﻴﺔ‬
‫اﻵﺧﺮ‬)Y(.‫وﻳﻼﺣﻘﻪ‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬ (‫)ﻳﺴﱰﺷﺪ‬ ‫ﻳﻜﺸﻒ‬ ‫أﻧﻪ‬ ‫ﺣﻴﺚ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻹﺳﱰﺷﺎدﻳﺔ‬ ‫ﺑﺎﳋﺎﺻﺔ‬ ‫ﻳﺴﻤﻰ‬ ‫ﻣﺎ‬ ‫وﻫﺬا‬
.‫اﳌﺆﺛﺮ‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬ ‫ﻣﻊ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﻣﻄﺎﺑﻘﺔ‬ ً‫ﻻ‬‫ﳏﺎو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﲟﺤﻮر‬
‫اﻟﻌﻼﻗﺘﲔ‬ ‫ﲨﻠﺔ‬ ‫ﻣﻦ‬(1.8):ً‫ﺎ‬‫أﻳﻀ‬ ‫ﻧﺴﺘﻨﺘﺞ‬
•‫اﳉﺎﻳﺮو‬ ‫ان‬‫ر‬‫دو‬ ‫ﻋﻨﺪ‬‫ﻫﺬﻩ‬ ‫ﰲ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫ﻓﺈن‬ ‫اﳊﺴﺎﺳﻴﺔ‬ ‫ﳏﻮري‬ ‫أﺣﺪ‬ ‫ﺣﻮل‬.‫اﻟﺰﻣﻦ‬ ‫ﻣﻊ‬ ً‫ﺎ‬‫ﺧﻄﻴ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫اﳊﺎﻟﺔ‬
•‫اﳉﺎﻳﺮو‬ ‫ان‬‫ر‬‫دو‬ ‫إن‬‫اﳉﺎﻳﺮو‬ ‫أن‬ ‫أي‬ .‫ﺑﺎﺧﺘﻔﺎﺋﻬﺎ‬ ‫وﳜﺘﻔﻲ‬ ‫اﻟﻌﺰوم‬ ‫ﻫﺬﻩ‬ ‫ﺑﻈﻬﻮر‬ ‫ﻳﻈﻬﺮ‬ ‫اﳋﺎرﺟﻴﺔ‬ ‫اﻟﻌﺰوم‬ ‫ﺑﺘﺄﺛﲑ‬
‫ﻋﻄﺎﱄ‬ ‫ﻻ‬ ‫ﺟﺴﻢ‬.‫ﺑﺎﻧﻌﺪاﻣﻪ‬ ‫وﺗﻨﻌﺪم‬ ً‫ﺎ‬‫ﺧﻄﻴ‬ ‫ﻟﻠﻌﺰم‬ ‫ﺗﺎﺑﻌﺔ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫اوﻳﺔ‬‫ز‬ ‫أن‬ ‫ﲟﻌﲎ‬

22. 21
‫ﺧﻮاص‬‫ﺧﻮاص‬‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫ﺳﻜﻮب‬‫ﺳﻜﻮب‬‫ﺛﻼﺛﻲ‬‫ﺛﻼﺛﻲ‬‫درﺟﺎت‬‫درﺟﺎت‬‫اﻟﺤﺮﻳﺔ‬‫اﻟﺤﺮﻳﺔ‬
(‫اﻧﻴﺔ‬‫ر‬‫دو‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺎت‬ ‫ﺛﻼث‬ ‫ﳝﺘﻠﻚ‬ ‫)أي‬ ‫وﺣﻴﺪة‬ ‫ﺗﻜﺎز‬‫ر‬‫ا‬ ‫ﻧﻘﻄﺔ‬ ‫اﱃ‬ ‫وﻳﺴﺘﻨﺪ‬ ‫ﻋﺎﻟﻴﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻳﺪور‬ ‫ﺻﻠﺐ‬ ‫ﺟﺴﻢ‬ ‫ﻛﻞ‬‫أن‬ ‫وﺟﺪﻧﺎ‬
.‫ﺧﺎرﺟﻴﺔ‬ ‫ﻋﺰوم‬ ‫ﻋﻠﻴﻪ‬ ‫ﺗﺆﺛﺮ‬ ‫ﱂ‬ ‫إذا‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫ﺛﺎﺑﺘﺎ‬ ‫ﻧﻪ‬‫ر‬‫ا‬‫و‬‫د‬ ‫ﳏﻮر‬ ‫ﻋﻠﻰ‬ ‫وﺑﺎﻟﺘﺎﱄ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬
.ً‫ﺎ‬‫ﺟﺎﻳﺮوﺳﻜﻮﺑﻴ‬ ً‫ﺎ‬‫ﺟﺴﻤ‬ ‫ﻋﻨﺪﻫﺎ‬ ‫اﳋﺎﺻﻴﺔ‬ ‫ﻫﺬﻩ‬ ‫ﳝﺘﻠﻚ‬ ‫اﻟﺬي‬ ‫اﳉﺴﻢ‬ ‫وﻳﺴﻤﻰ‬
:‫اﻟﺨﺼﺎﺋﺺ‬ ‫ﻫﺬﻩ‬ ‫أﻫﻢ‬ ‫وﻣﻦ‬ .‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﻲ‬ ‫ﻏﻴﺮ‬ ‫اﻟﺼﻠﺐ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻋﻦ‬ ‫ﺗﻤﻴﺰﻩ‬ ‫ﻋﺪﻳﺪﻩ‬ ‫ﺑﺨﺼﺎﺋﺺ‬ ‫اﻟﺠﺎﻳﺮو‬ ‫ﻳﺘﻤﻴﺰ‬
‫اﻻﺳﺘﻘﻼل‬‫اﻟﺠﺴﻢ‬ ‫ﻋﻦ‬‫اﻟﺤﺎﻣﻞ‬:
‫أي‬‫ﻣﻨﺤﻰ‬ ‫ﻋﻠﻰ‬ ‫اﶈﺎﻓﻈﺔ‬(‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﳏﻮر‬ ‫)اﲡﺎﻩ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬‫ﻋﻨﺪ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬‫ﻏﻴﺎب‬‫اﻟﻌﺰوم‬ ‫ﺗﺄﺛﲑ‬
.‫اﳋﺎرﺟﻴﺔ‬‫ﻛﻴﻔﻤﺎ‬‫اﻹﺑﺘﺪاﺋﻴﺔ‬ ‫ﳊﺎﻟﺘﻪ‬ ً‫ﺎ‬‫ﻳ‬‫ز‬‫ا‬‫ﻮ‬‫ﻣ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫اﻷﺳﺎﺳﻲ‬ ‫ﶈﻮرﻩ‬ ‫ﺗﻮﺟﻪ‬ ‫ﻋﻠﻰ‬ ‫ﳛﺎﻓﻆ‬ ‫اﳊﺮ‬ ‫اﳉﺎﻳﺮو‬ ‫أن‬ ‫أي‬
.‫اﳊﺎﻣﻞ‬ ‫اﳉﺴﻢ‬ ‫ﲢﺮك‬
‫اﻟﺨﺎﺻﺔ‬:‫اﻻﺳﺘﺮﺷﺎدﻳﺔ‬
‫اﳊﺴﺎﺳﻴﺔ‬ ‫ﳏﻮر‬ ‫ﺣﻮل‬ ‫ﻳﺪور‬ ‫اﳉﺎﻳﺮو‬ ‫ﻓﺈن‬ ‫ﺣﺴﺎﺳﻴﺘﻪ‬ ‫ﳏﺎور‬ ‫أﺣﺪ‬ ‫ﺣﻮل‬ ‫ﺧﺎرﺟﻲ‬ ‫ﻋﺰم‬ ‫ﻟﺘﺄﺛﲑ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺗﻌﺮض‬ ‫ﻣﺎ‬ ‫إذا‬
‫ﻣﻊ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﻣﻄﺎﺑﻘﺔ‬ ‫ﺑﺬﻟﻚ‬ ً‫ﻻ‬‫ﳏﺎو‬ ‫اﳌﻄﺒﻖ‬ ‫اﻟﻌﺰم‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬ (‫اﻻﺳﱰﺷﺎد‬ ‫)ﺳﺮﻋﺔ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻵﺧﺮ‬
‫ﻛﺔ‬‫ﺑﺎﳊﺮ‬ ‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻫﺬﻩ‬ ‫وﺗﺴﻤﻰ‬ ‫ﻋﻠﻴﻪ‬ ‫اﳌﻄﺒﻖ‬ ‫اﳋﺎرﺟﻲ‬ ‫ﺑﺎﻟﻌﺰم‬ ‫ﻳﺴﱰﺷﺪ‬ ‫اﳉﺎﻳﺮو‬ ‫إن‬ ‫ﻋﻨﺪﻫﺎ‬ ‫ﻧﻘﻮل‬ .‫اﳌﻄﺒﻖ‬ ‫اﻟﻌﺰم‬ ‫اﲡﺎﻩ‬
.‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻔﻀﺎء‬ ‫ﰲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻟﺘﻮﺟﻴﻪ‬ ‫اﳋﺎﺻﺔ‬ ‫ﻫﺬﻩ‬ ‫ﺗﺴﺘﺨﺪم‬ .‫اﻻﺳﱰﺷﺎدﻳﺔ‬
) ‫ﻟﻠﺸﻜﻞ‬ ً‫ﺎ‬‫وﻓﻘ‬3-1‫ﺧﺎرﺟﻲ‬ ‫ﻋﺰم‬ ‫إﱃ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻹﻃﺎر‬ ‫ﺗﻌﺮض‬ ‫إذا‬ (yM‫اﳋﺎرﺟﻲ‬ ‫اﻹﻃﺎر‬ ‫ﺗﺪوﻳﺮ‬ ً‫ﻻ‬‫ﳏﺎو‬
‫اﻻﺳﺘﻨﺎد‬ ‫ﳏﻮر‬ ‫ﺣﻮل‬ ‫اﳉﺎﻳﺮو‬‫و‬ ‫اﻟﺪاﺧﻠﻲ‬ ‫اﻹﻃﺎر‬ ‫ﻣﻊ‬Y‫ﺣﻮل‬ ‫ﻳﺪور‬ ‫ﻟﻦ‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﺧﻼف‬ ‫ﻋﻠﻰ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻓﺈن‬
‫اﶈﻮر‬Y‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اﻟﺪاﺧﻠﻲ‬ ‫إﻃﺎرﻩ‬ ‫ﻣﻊ‬ ‫ﺳﻴﺪور‬ ‫وإﳕﺎ‬X‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬
H
My
x =ω‫)ﺣﻴﺚ‬)(H‫اﻟﻌﺰم‬
‫ﻛﻲ‬‫اﳊﺮ‬ ‫ﻋﺰﻣﻪ‬ ‫ﺷﻌﺎع‬ ‫ﻣﻄﺎﺑﻘﺔ‬ ً‫ﻻ‬‫ﳏﺎو‬ (‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬)(H‫اﳌﻄﺒﻖ‬ ‫اﻟﻌﺰم‬ ‫ﻣﻊ‬yM‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻫﺬﻩ‬ ‫ﺗﻘﻴﺪ‬ ‫ﱂ‬ ‫وإذا‬
‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬ ‫ﻓﺈن‬ ‫اﻻﺳﱰﺷﺎدﻳﺔ‬)(H‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫اﲡﺎﻩ‬ ‫ﻣﻊ‬ ‫اﳌﻄﺎف‬ ‫�ﺎﻳﺔ‬ ‫ﰲ‬ ‫ﻳﻨﻄﺒﻖ‬ ‫ﺳﻮف‬ ‫ﻟﻠﺠﺎﻳﺮو‬

23. 22
yM‫ﺗﻘﻴﻴﺪ‬ ‫إﱃ‬ ‫ﻋﺎدة‬ ‫ﻳﺼﺎر‬ ‫وﻟﺬﻟﻚ‬ ‫اﳊﺮ‬ ‫اﳉﺎﻳﺮو‬ ‫اص‬‫ﻮ‬‫ﺧ‬ ‫وﻳﻔﻘﺪ‬ ‫ﻳﺘﻪ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺎت‬ ‫إﺣﺪى‬ ‫اﳉﺎﻳﺮو‬ ‫ﻳﻔﻘﺪ‬ ‫وﺑﺬﻟﻚ‬
‫ﺗﺜﺒﻴﺖ‬ ‫اﺑﺾ‬‫ﻮ‬‫ﻧ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﳉﺎﻳﺮو‬ ‫ات‬‫ر‬‫إﻃﺎ‬ ‫ﻛﺔ‬‫ﺣﺮ‬ ‫ﺗﻘﻴﻴﺪ‬ ‫ﻳﻖ‬‫ﺮ‬‫ﻃ‬ ‫ﻋﻦ‬ ‫اﳌﺨﺘﻠﻔﺔ‬ ‫ﺗﻄﺒﻴﻘﺎﺗﻪ‬ ‫ﰲ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻻﺳﱰﺷﺎدﻳﺔ‬ ‫ﻛﺔ‬‫اﳊﺮ‬
.(‫ﻋﺰم‬ ‫ﻣﻮﻟﺪ‬ ،‫ﻣﻀﺨﻢ‬ ،‫اوﻳﺔ‬‫ز‬ ‫)ﺣﺴﺎس‬ ‫ﺑﺎﺋﻴﺔ‬‫ﺮ‬‫ﻛﻬ‬‫ﺗﺜﺒﻴﺖ‬ ‫اﺑﺾ‬‫ﻮ‬‫ﻧ‬ ‫أو‬ ‫ﻣﻴﻜﺎﻧﻴﻜﻴﺔ‬
‫اﻟﺨﺎﺻﺔ‬:‫اﻟﻼﻋﻄﺎﻟﻴﺔ‬
‫ﺗﻌﺮ‬ ‫ﻣﺎ‬ ‫ﻓﺈذا‬ ‫ﻻﻋﻄﺎﱄ‬ ‫ﺟﺴﻢ‬ ‫ﻫﻮ‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﺧﻼف‬ ‫ﻋﻠﻰ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮب‬‫ض‬‫ﻓﺈﻧﻪ‬ ‫ﺧﺎرﺟﻴﺔ‬ ‫ﻋﺰوم‬ ‫ﻟﺘﺄﺛﲑ‬ ‫اﳉﺎﻳﺮو‬
‫ﺣﺴﺚ‬ .‫اﻟﻌﺰوم‬ ‫ﻫﺬﻩ‬ ‫ﺗﺄﺛﲑ‬ ‫ال‬‫و‬‫ز‬ ‫ﻋﻨﺪ‬ ‫اﻷﺧﲑ‬ ‫ﺗﻮﺟﻬﻪ‬ ‫ﻋﻠﻰ‬ ‫وﳛﺎﻓﻆ‬ ‫اف‬‫ﺮ‬‫اﻻﳓ‬ ‫ﻋﻦ‬ ‫ﻳﺘﻮﻗﻒ‬ ‫ﻟﻜﻨﻪ‬ ‫ﻬﺑﺎ‬ ً‫ا‬‫ﻣﺴﱰﺷﺪ‬ ‫ﻳﻨﺤﺮف‬
‫اﻟﻌﺰم‬ ‫ﻣﻊ‬ ً‫ا‬‫ﻃﺮد‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬ ‫اﻵﺧﺮ‬ ‫اﶈﻮر‬ ‫ﻋﻠﻰ‬ ‫ﺳﺮﻋﺔ‬ ،‫ﳏﻮر‬ ‫ﺣﻮل‬ ‫ﺧﺎرﺟﻲ‬ ‫ﻟﻌﺰم‬ ‫ﺗﻌﺮﺿﻪ‬ ‫ﻋﻨﺪ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﰊ‬ ‫اﳉﺴﻢ‬ ‫ﻳﻜﺘﺴﺐ‬
‫ﺗﻌﺮ‬ ‫ﻣﺎ‬ ‫إذا‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﻷن‬ ‫ذﻟﻚ‬ .‫ﻟﻠﺠﺴﻢ‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﻣﻊ‬ ً‫ﺎ‬‫وﻋﻜﺴ‬ ‫اﳌﻄﺒﻖ‬‫ض‬‫ﺧﺎرﺟﻲ‬ ‫ﻟﻌﺰم‬)(My‫ﻓﺈﻧﻪ‬
‫اوﻳﺎ‬‫ز‬ ً‫ﺎ‬‫ﺗﺴﺎرﻋ‬ ‫ﺳﻴﻜﺘﺴﺐ‬
I
M y
y =α‫)ﺣﻴﺚ‬)(I‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫ال‬‫و‬‫ﺑﺰ‬ ،(‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﻋﻄﺎﻟﺔ‬ ‫ﻋﺰم‬( )0=yM
‫اوي‬‫ﺰ‬‫اﻟ‬ ‫ع‬‫اﻟﺘﺴﺎر‬ ‫ﺳﻴﻨﻌﺪم‬)( yα‫اﳌﻜﺘﺴﺒﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫وﺳﻴﺤﺎﻓﻆ‬)( yα‫اﻟﻌﺰم‬ ‫ال‬‫و‬‫ز‬ ‫ﳊﻈﺔ‬
‫وﻟﻜﻦ‬ ‫ﺳﻴﺘﻮﻗﻒ‬ ‫ﻓﺈﻧﻪ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻗﻮى‬ ‫ﻛﺘﻪ‬‫ﺣﺮ‬ ‫ﻗﺎوﻣﺖ‬ ‫وإذا‬ ‫أﺧﺮى‬ ‫ﺧﺎرﺟﻴﺔ‬ ‫ﻋﺰوم‬ ‫ﻋﻠﻴﻪ‬ ‫ﺗﺆﺛﺮ‬ ‫ﱂ‬ ‫ﻣﺎ‬ ‫ان‬‫ر‬‫ﺑﺎﻟﺪو‬ ً‫ا‬‫ﺮ‬‫ﻣﺴﺘﻤ‬ ‫اﳋﺎرﺟﻲ‬
‫ﺧﺎرﺟﻲ‬ ‫ﻟﻌﺰم‬ ‫ﺗﻌﺮﺿﻪ‬ ‫ﻋﻨﺪ‬ ‫ﻓﺈﻧﻪ‬ ‫اﳉﺎﻳﺮو‬ ‫أﻣﺎ‬ .‫ﳏﺪد‬ ‫أﺟﻞ‬ ‫ﺑﻌﺪ‬)( yM‫اﶈﻮر‬ ‫ﻋﻠﻰ‬)(Y‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ﺳﻴﺪور‬ ‫ﻓﺈﻧﻪ‬)(X
‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬
H
M y
x =ω‫)ﺣﻴﺚ‬)(H‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫ال‬‫و‬‫ﺑﺰ‬ .(‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬( )0=yM‫اﻟﺴﺮﻋﺔ‬ ‫ﺳﺘﻨﻌﺪم‬
‫ﻟﻠﺠﺎﻳﺮو‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬)( xω‫اﲡﺎﻫﻪ‬ ‫ﻋﻠﻰ‬ ً‫ﺎ‬‫ﳏﺎﻓﻈ‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫ﺗﺄﺛﲑ‬ ‫ال‬‫و‬‫ز‬ ‫ﳊﻈﺔ‬ ‫ﻣﺒﺎﺷﺮة‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻋﻦ‬ ‫اﳉﺎﻳﺮو‬ ‫وﺳﻴﺘﻮﻗﻒ‬
.‫ﻋﻄﺎﻟﻴﺔ‬ ‫ﻟﻪ‬ ‫ﻟﻴﺲ‬ ‫اﻟﺼﻠﺒﺐ‬ ‫ﻟﻠﺠﺴﻢ‬ ً‫ﺎ‬‫ﺧﻼﻓ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻓﺈن‬ ‫ﻟﺬﻟﻚ‬ .‫أﺧﺮى‬ ‫ﺧﺎرﺟﻴﺔ‬ ‫ﻋﺰوم‬ ‫ﻋﻠﻴﻪ‬ ‫ﺗﺆﺛﺮ‬ ‫ﱂ‬ ‫ﻣﺎ‬ ‫اﻷﺧﲑ‬
‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻳﺘﺼﻒ‬ ‫ﺑﻴﻨﻤﺎ‬ ،‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻼﺛﻲ‬ ‫ﻟﻠﺤﺎﻳﺮو‬ ‫اﻟﻌﺎﻣﺔ‬ ‫اص‬‫ﻮ‬‫اﳋ‬ ‫ﻫﺬﻩ‬ ‫ﲤﺜﻞ‬‫اص‬‫ﻮ‬‫ﺑﺎﳋ‬
.‫ﻓﻘﻂ‬ ‫اﳊﺮ‬ ‫اﳉﺎﻳﺮو‬ ‫ﲤﻴﺰ‬ ‫اﻟﱵ‬ ‫اﻷوﱃ‬ ‫اﻟﺼﻔﺔ‬ ‫ﻋﺪا‬ ‫ﻣﺎ‬ ‫ذاﻬﺗﺎ‬

24. 23
‫ﻣﻘﺎرﻧﺔ‬‫ﻣﻘﺎرﻧﺔ‬‫ﺑﻴﻦ‬‫ﺑﻴﻦ‬‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫واﻟﺠﺴﻢ‬‫واﻟﺠﺴﻢ‬‫اﻟﺼﻠﺐ‬‫اﻟﺼﻠﺐ‬
‫ﻳﺒﲔ‬‫اﳉﺪول‬)1(‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﳉﺴﻢ‬‫و‬ ‫اﻟﻌﺎدي‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﺑﲔ‬ ‫اﻷﺳﺎﺳﻴﺔ‬ ‫ارق‬‫ﻮ‬‫اﻟﻔ‬ ‫ﺧﻼﺻﺔ‬‫ﻻﺳﺘﻴﻀﺎح‬ ‫وذﻟﻚ‬ ،
.‫اﳉﺎﻳﺮو‬ ‫ﺧﺼﻮﺻﻴﺎت‬ ‫وﺗﺒﲔ‬ ،‫اﳉﺴﻤﲔ‬ ‫ﻫﺬﻳﻦ‬ ‫ﺑﲔ‬ ‫ﺋﻴﺴﺔ‬‫ﺮ‬‫اﻟ‬ ‫اﻟﻔﺮوق‬
‫ﳏﺎور‬ ‫ﺑﲔ‬ ‫ﻣﺘﺼﺎﻟﺒﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ـﻨﺘﺞ‬ُ‫ﻳ‬ ‫اﻟﺬي‬‫و‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﻟﻠﻌﺰم‬ ‫اﳌﻤﺜﻞ‬ ‫اﳊﺪ‬ ‫ﻇﻬﻮر‬ ‫ﻫﻮ‬ ‫اﻷﺳﺎﺳﻲ‬ ‫اﻟﻔﺮق‬ ‫أن‬ ‫اﺿﺢ‬‫ﻮ‬‫اﻟ‬ ‫ﻣﻦ‬
.‫اﻟﺘﻘﻠﻴﺪي‬ ‫اﻟﺼﻠﺐ‬ ‫اﳉﺴﻢ‬ ‫ﰲ‬ ‫اﳌﻮﺟﻮد‬ ‫اﶈﺎور‬ ‫اﺳﺘﻘﻼﻟﻴﺔ‬ ‫ﻣﺒﺪأ‬ ‫ﻟﺘﻨﻘﺾ‬ ‫ان‬‫ر‬‫اﻟﺪو‬
‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫اﻟﺨﺎﺻﺔ‬‫اﻟﺼﻠﺐ‬ ‫اﻟﺠﺴﻢ‬‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﻲ‬ ‫اﻟﺠﺴﻢ‬
‫ﻛﺔ‬‫اﻟﺤﺮ‬ ‫ﻗﺎﻧﻮن‬XXX IM θ.=
YXZYY
XYZXX
MHI
MHI
=⋅−⋅
=⋅+⋅
θθ
θθ


‫اﻟﻌﺰوم‬ ‫ﻋﻼﻗﺔ‬‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻌﺰم‬ ‫ﻳﺴﺎوي‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬
‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻌﺰم‬ ‫ﻳﺴﺎوي‬ ‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬
‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫إﻟﻴﻪ‬ ً‫ﺎ‬‫ﻣﻀﺎﻓ‬
‫أﺣﺪ‬ ‫ﺣﻮل‬ ‫ﺧﺎرﺟﻲ‬ ‫ﻋﺰم‬ ‫ﺑﺘﺄﺛﻴﺮ‬
‫ﻣﺤﺎورﻩ‬
‫اﶈﻮر‬ ‫ﻧﻔﺲ‬ ‫ﺣﻮل‬ ‫ﻳﺪور‬‫اوي‬‫ز‬ ‫ع‬‫ﺑﺘﺴﺎر‬
‫اﻟﻌﺰم‬ ‫ذﻟﻚ‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺐ‬
‫اﳌﺘﻌﺎﻣﺪ‬‫و‬ ‫ﻟﻪ‬ ‫اﳌﻌﺎﻣﺪ‬ ‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ﻳﺪور‬
‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬ ‫ﺷﻌﺎع‬ ‫ﻣﻊ‬‫اوﻳﺔ‬‫ز‬ ‫وﺑﺴﺮﻋﺔ‬
‫اﻟﻌﺰم‬ ‫ذﻟﻚ‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬
‫اﻟﺨﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬ ‫ﺗﺄﺛﻴﺮ‬ ‫ﺑﺎﺧﺘﻔﺎء‬‫ﻋﻄﺎﻟﺘﻪ‬ ‫ﺑﺘﺄﺛﲑ‬ ‫ان‬‫ر‬‫ﺑﺎﻟﺪو‬ ‫ﻳﺴﺘﻤﺮ‬‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻋﻦ‬ ً‫ا‬‫ر‬‫ﻓﻮ‬ ‫ﻳﺘﻮﻗﻒ‬
‫اﻟﺰﻣﻦ‬ ‫ﻣﻊ‬ ‫اﻟﺰاوﻳﺔ‬ ‫ﺗﻐﻴﺮ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻊ‬‫ﺮ‬‫ﻣ‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺐ‬‫اﻟﺰﻣﻦ‬ ‫ﻣﻊ‬ ‫ﺧﻄﻲ‬

25. 24
‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫أﻧﻮاع‬‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫أﻧﻮاع‬
‫ﰲ‬ ً‫ﺎ‬‫اﺳﻌ‬‫و‬ ً‫ﺎ‬‫ﺗﻨﻮﻋ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺘﻨﻮع‬‫و‬ ،‫ﻳﺘﻬﺎ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺔ‬‫اﳌﺒﺎدئ‬ ‫وﰲ‬ ،‫ﺗﻘﻴﺴﻬﺎ‬ ‫اﻟﱵ‬ ‫ﻳﺎﺋﻴﺔ‬‫ﺰ‬‫اﻟﻔﻴ‬ ‫اﻟﻘﻴﻤﺔ‬ ‫وﰲ‬ ،‫ﻋﻤﻠﻬﺎ‬ ‫ﻣﺒﺪأ‬
‫ﺑﺘﻴﺎر‬ ،‫اﻣﻦ‬‫ﺰ‬‫ﻣﺘ‬ ‫ﻻ‬ ،‫اﻣﻦ‬‫ﺰ‬‫)ﻣﺘ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﶈﺮك‬ ‫ﺗﺼﻤﻴﻢ‬ ‫ﰲ‬ ‫اﳌﻌﺘﻤﺪة‬ ‫ﻳﻘﺔ‬‫ﺮ‬‫اﻟﻄ‬ ‫وﰲ‬ ،‫ﻛﺔ‬‫اﳊﺮ‬‫و‬ ‫اﻻﺳﺘﻨﺎد‬ ‫ﰲ‬ ‫اﳌﻌﺘﻤﺪة‬ ‫ﻳﺎﺋﻴﺔ‬‫ﺰ‬‫اﻟﻔﻴ‬
.(‫ﻣﺴﺘﻤﺮ‬
‫اﳌﺼﻤﻤﲔ‬ ‫اﺟﻪ‬‫ﻮ‬‫ﺗ‬ ‫اﻟﱵ‬ ‫اﻟﺼﻌﻮﺑﺎت‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺨﻠﺺ‬ ‫اﻟﻄﺮق‬ ‫ﳐﺘﻠﻒ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻫﻮ‬ ‫اﺳﻊ‬‫ﻮ‬‫اﻟ‬ ‫اﻟﺘﻨﻮع‬ ‫ﻫﺬا‬ ‫ﺳﺒﺐ‬‫)ﻛﺘﺤﻘﻴﻖ‬
(‫اﳋﺎرﺟﻴﺔ‬ ‫اﻟﻌﺰوم‬ ‫ﻣﻦ‬ ‫اﳉﺴﻢ‬ ‫وﲪﺎﻳﺔ‬ ،‫اﻟﺴﺮﻋﺔ‬ ‫ﻫﺬﻩ‬ ‫ﻋﻠﻰ‬ ‫اﶈﺎﻓﻈﺔ‬‫و‬ ،‫ﻋﺎﻟﻴﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫وﺗﺪوﻳﺮﻩ‬ ،‫ﻛﺔ‬‫ﻣﺘﺤﺮ‬ ‫ﻏﲑ‬ ‫ﻧﻘﻄﺔ‬ ‫ﳝﻠﻚ‬ ‫ﺟﺴﻢ‬
.‫اﻷﻣﺜﻞ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻟﻠﻮﺻﻮل‬ ‫ﳏﺎوﻟﺔ‬ ‫ﰲ‬ ،‫أﻛﱪ‬ ‫دﻗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫وذﻟﻚ‬
‫وﺻﻠﺔ‬ ‫ﳏﺎور‬ ‫ﺣﻮل‬ ‫اﳋﺎرﺟﻴﺔ‬ ‫اﻟﻌﺰوم‬ ‫ﺗﻘﻠﻴﻞ‬ ‫ﻣﻦ‬ ‫ﺑﺪ‬ ‫ﻻ‬ – ‫اﳉﺎﻳﺮو‬ ‫ﻣﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫ﻧﺘﺒﲔ‬ ‫ﻛﻤﺎ‬ – ‫اﳌﺬﻛﻮر‬ ‫ﻟﻠﻬﺪف‬ ‫ﻟﻠﻮﺻﻮل‬
.‫اﻟﻮﺻﻠﺔ‬ ‫ﳍﺬﻩ‬ ‫اﻟﻌﻄﺎﱄ‬ ‫اﻟﻌﺰم‬ ‫وﺗﻘﻠﻴﻞ‬ ،‫ﻛﺎردان‬.‫اﳍﺪف‬ ‫ﻫﺬا‬ ‫ﻟﺘﺤﻘﻴﻖ‬ ‫اﻟﻌﻠﻮم‬‫و‬ ‫اﻟﺘﻘﻨﻴﺎت‬ ‫ﳐﺘﻠﻒ‬ ‫اﺳﺘﺨﺪﻣﺖ‬ ‫وﻗﺪ‬
•‫اﻟﻔﺌﺎت‬ ‫ﰲ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺼﻨﻴﻒ‬ ‫ﳝﻜﻦ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻋﻤﻞ‬ ‫ﻣﺒﺪأ‬ ‫ﺣﺴﺐ‬‫ﺋﻴﺴﺔ‬‫ﺮ‬‫اﻟ‬:‫اﻟﺘﺎﻟﻴﺔ‬
1.‫اﳉﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫اﻹﻟﻜﱰوﻣﻴﻜﺎﻧﻴﻜﻲ‬‫اﻟﺘﻘﻠﻴﺪﻳﺔ‬ ‫ة‬
2.‫اﳉﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫ازي‬‫ﺰ‬‫اﻻﻫﺘ‬‫ة‬
3.‫اﳉﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫اﻟﻀﻮﺋﻲ‬‫ة‬
•‫ﺣﺴﺐ‬‫ار‬‫و‬‫د‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺔ‬‫اﳉﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺼﻨﻴﻒ‬ ‫ﳝﻜﻦ‬ ‫اﳉﺎﻳﺮو‬‫إﱃ‬:
1..‫أﻋﻼﻩ‬ ‫اﺳﺘﻪ‬‫ر‬‫د‬ ‫ﲤﺖ‬ ‫وﻗﺪ‬ ‫اﳊﺮ‬ ‫اﳉﺎﻳﺮو‬ ‫أو‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻼﺛﻲ‬ ‫ﺟﺎﻳﺮو‬
2..‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫ﺟﺎﻳﺮو‬

26. 25
‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫ﺛﻨﺎﺋﻲ‬‫ﺛﻨﺎﺋﻲ‬‫درﺟﺎت‬‫درﺟﺎت‬‫اﻟﺤﺮﻳﺔ‬‫اﻟﺤﺮﻳﺔ‬
‫ﺷﻌﺎع‬ ‫ﻣﻊ‬ ‫ﻟﻠﺘﻄﺎﺑﻖ‬ ‫اﻟﺬاﰐ‬ ‫ﳏﻮرﻩ‬ ‫وﺳﻴﺴﻌﻰ‬ ،‫اﳉﺎﻳﺮﺳﻜﻮﺑﻴﺔ‬ ‫اص‬‫ﻮ‬‫اﳋ‬ ‫ﺑﺒﻌﺾ‬ ‫ﳛﺘﻔﻆ‬ ‫ﻓﺈﻧﻪ‬ ‫ﻳﺔ‬‫ﺮ‬‫ﺣ‬ ‫درﺟﺔ‬ ‫اﳊﺮ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺳﻠﺒﻨﺎ‬ ‫إذا‬
‫ﳓﺼﻞ‬ ‫أن‬ ‫ﳝﻜﻦ‬ ‫ﻋﻠﻴﻪ‬ ‫اﻹﺿﺎﻓﺎت‬ ‫ﺣﺴﺐ‬ ‫وﻋﻨﺪﻫﺎ‬ ‫ﳐﻤﺪ‬ ‫أو‬ ‫ﻧﺎﺑﺾ‬ ‫إﻣﺎ‬ ‫إﺿﺎﻓﺔ‬ ‫ﻣﻦ‬ ‫ﺑﺪ‬ ‫ﻻ‬ ‫ذﻟﻚ‬ ‫ﻹﻳﻘﺎف‬ ،‫اﳋﺎرﺟﻲ‬ ‫اﻟﻌﺰم‬
‫وإذا‬ .‫اوﻳﺔ‬‫ز‬ ‫ﺳﺮﻋﺔ‬ ‫ﺣﺴﺎس‬ ‫ﻋﻠﻰ‬ ‫ﳓﺼﻞ‬ ً‫ﺎ‬‫ﻧﺎﺑﻀ‬ ‫أﺿﻔﻨﺎ‬ ‫ﻓﺈذا‬ .‫ﻣﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺳﺮﻋﺔ‬ ‫ﺣﺴﺎس‬ ‫أو‬ ‫ﻣﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺣﺴﺎس‬ ‫ﻋﻠﻰ‬
. .‫ﻳﻠﻲ‬ ‫ﻓﻴﻤﺎ‬ ‫ﺳﻴﺘﺒﲔ‬ ‫ﻛﻤﺎ‬‫اوﻳﺔ‬‫ز‬ ‫ﺣﺴﺎس‬ ‫ﻋﻠﻰ‬ ‫ﳓﺼﻞ‬ ً‫ا‬‫ﳐﻤﺪ‬ ‫أﺿﻔﻨﺎ‬
‫اﻟﻤﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺣﺴﺎس‬:‫ﻋﻠﻰ‬ ‫اﳉﲑﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﻧﺔ‬‫ز‬‫ا‬‫ﻮ‬‫ﳌ‬ ‫ﻛﺎﰲ‬‫ﻧﺎﺑﺾ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫أﺿﻔﻨﺎ‬ ‫إذا‬
‫اﶈﻮر‬X‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻣﺘﺤﺮك‬ ‫ﻣﻜﺎن‬ ‫ﻋﻠﻰ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻛﻨﺎ‬‫وﺗﺮ‬ .Y‫ﻗﻴﻤﺘﻬﺎ‬θω‫ﻳﺒﺪأ‬ ‫ﺳﻮف‬ ‫اﳉﺎﻳﺮو‬ ‫ﻓﺈن‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ﺑﺎﻹﺳﱰﺷﺎد‬X‫ﻧﺘﻴﺠﺔ‬ .‫ﻟﻠﻨﺎﺑﺾ‬ ‫اﳌﺮوﱐ‬ ‫اﻟﻌﺰم‬ ‫ﻣﻊ‬ ‫ازن‬‫ﻮ‬‫ﻳﺘ‬ ‫اﻟﺬي‬‫و‬ ‫ﺣﻮﻟﻪ‬ ‫اﳌﺘﺸﻜﻞ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﺑﺴﺒﺐ‬
‫اوﻳﺔ‬‫ﺰ‬‫ﺑ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻟﺬاﰐ‬ ‫اﶈﻮر‬ ‫ﻳﻨﺤﺮف‬ ‫ﻟﺬﻟﻚ‬ϕ‫اﳌﺆﺛﺮة‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬θω.
)‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬9‫ﺟﺴﺎﺳﻴﺘﻪ‬ ‫ﳏﻮر‬ ‫ﻋﻠﻰ‬ ‫ﻧﺎﺑﺾ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻣﻊ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ (X.
‫اﻟﺸﻜﻞ‬7.‫اوﻳﺔ‬‫ز‬ ‫ﺳﺮﻋﺔ‬ ‫ﻣﻘﻴﺎس‬ = ‫ﺑﻨﺎﺑﺾ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫ﺟﺎﻳﺮو‬ :
:‫ﻳﻠﻲ‬ ‫ﳑﺎ‬ ‫اﳊﺴﺎس‬ ‫ﻳﺘﻜﻮن‬

27. 26
1..‫اﳍﻴﻜﻞ‬
2..‫اﻟﻨﺎﺑﺾ‬
3..(‫از‬‫ﺰ‬‫اﻻﻫﺘ‬ ‫ﲣﻤﻴﺪ‬ ‫ﺑﺪور‬ ‫ﻓﻘﻂ‬ ‫)ﻳﻘﻮم‬ ‫ج‬‫ﻟﺰ‬ ‫ﳐﻤﺪ‬
4..‫إﻃﺎر‬
5..‫اﻟﺪاﺋﺮ‬
6..‫اﻹﻃﺎر‬ ‫ج‬‫ﺧﺮ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﻣﺒﲔ‬
:‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﺣﻞ‬‫ﺮ‬‫اﳌ‬ ‫وﻓﻖ‬ ‫اﳊﺴﺎس‬ ‫ﻳﻌﻤﻞ‬
1.‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﳊﺎﻣﻞ‬ ‫ان‬‫ر‬‫دو‬ ‫ﻋﻨﺪ‬Y‫ﻗﻴﻤﺘﻬﺎ‬θω‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﻋﺰم‬ ‫ﺳﻴﻈﻬﺮ‬GM‫ﻳﺘﻨﺎﺳﺐ‬‫ﻣﻊ‬
:‫اﳌﻌﺎدﻟﺔ‬ ‫وﻓﻖ‬ ‫اﳌﻘﺎﺳﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬
. . sin( ) .GM H Hθ θω ϕ ω= ≈
) ‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﳌﺒﲔ‬ ‫اﻹﲡﺎﻩ‬ ‫ﰲ‬ ‫وذﻟﻚ‬8‫ﺣﻴﺚ‬ .(H.(‫ﻛﺔ‬‫اﳊﺮ‬ ‫ﻛﻤﻴﺔ‬‫ﻋﺰم‬ ‫أي‬ ) ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬
2.‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﻳﺆدي‬GM‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫وﺳﺮﻋﺔ‬ ‫اوي‬‫ز‬ ‫ع‬‫ﺗﺴﺎر‬ ‫ﻟﻈﻬﻮر‬X‫اوﻳﺔ‬‫ز‬ ‫ﻟﻈﻬﻮر‬ ‫ﻳﺆدي‬ ‫ﳑﺎ‬
ϕ.
3.‫اوﻳﺔ‬‫ز‬ ‫ﻇﻬﻮر‬ ‫ﻳﺆدي‬ϕ:‫ﻳﺴﺎوي‬ ‫اﻟﻨﺎﺑﺾ‬ ‫ﰲ‬ ‫ﻣﺮوﱐ‬ ‫ﻋﺰم‬ ‫ﺗﺸﻜﻞ‬ ‫إﱃ‬
.CM C ϕ=
‫ﺣﻴﺚ‬ .‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﳉﻬﺔ‬ ‫اﳌﻌﺎﻛﺲ‬‫و‬ ،‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﳌﺒﲔ‬ ‫اﻹﲡﺎﻩ‬ ‫ﰲ‬ ‫وذﻟﻚ‬C.‫اﻟﻨﺎﺑﺾ‬ ‫ﺻﻼﺑﺔ‬ ‫ﺛﺎﺑﺖ‬
4.) ‫ج‬‫اﻟﻠﺰ‬ ‫اﳌﺨﻤﺪ‬ ‫ﻳﻌﻬﺎ‬‫ﺮ‬‫ﺗﺴ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻌﻤﻞ‬ ‫اﻟﱵ‬ ‫اﻟﻌﺎﺑﺮة‬ ‫اءات‬‫ﺮ‬‫اﻹﺟ‬ ‫ﲣﺎﻣﺪ‬ ‫ﻋﻨﺪ‬3:‫وﻳﺼﺒﺢ‬ ‫اﻟﻌﺰﻣﲔ‬ ‫ازن‬‫ﻮ‬‫ﺳﻴﺘ‬ (
. .
.
C G
H
C
M C M H θ
θ
ϕ ω
ϕ ω
= = = ⇒
=
.‫ﻟﻠﺤﺎﻣﻞ‬ ‫اﳌﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫ﺣﺴﺎس‬ ‫ﻳﻘﻴﺴﻬﺎ‬ ‫اﻟﱵ‬‫و‬ ‫اﳌﺘﺸﻜﻠﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫أن‬ ‫أي‬
.‫ﻋﺰم‬ ‫وﻣﻮﻟﺪ‬ ‫وﻣﻀﺨﻢ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺣﺴﺎس‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ً‫ﺎ‬‫ﺑﺎﺋﻴ‬‫ﺮ‬‫ﻛﻬ‬‫أو‬ ً‫ﺎ‬‫ﻣﻴﻜﺎﻧﻴﻜﻴ‬ ‫اﻟﻨﺎﺑﺾ‬ ‫ﻳﻜﻮن‬ ‫أن‬ ‫ﳝﻜﻦ‬

28. 27
) ‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬10‫اء‬‫ﺰ‬‫اﻷﺟ‬ ‫ﻣﻦ‬ ‫ﻳﺘﻜﻮن‬ ‫اﻟﺬي‬‫و‬.‫اﺋﻴﺔ‬‫ﻮ‬‫ﻫ‬ ‫ﻋﻨﻔﺔ‬ ‫اﺳﻄﺔ‬‫ﻮ‬‫ﺑ‬ ‫ﻳﻌﻤﻞ‬ ‫اﻟﺬي‬ ‫اﳌﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺒﲔ‬ ‫ﻋﻠﻰ‬ ً‫ﻻ‬‫ﻣﺜﺎ‬ (
:‫اﻟﺘﺎﻟﻴﺔ‬ ‫ﺋﻴﺴﻴﺔ‬‫ﺮ‬‫اﻟ‬
‫اﻟﺸﻜﻞ‬8‫اﳌﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺒﲔ‬ :
1..‫اﻟﻨﺎﺑﺾ‬ ‫ﺷﺪ‬ ‫ﻣﻌﺎﻳﺮة‬ ‫ﺑﺮﻏﻲ‬
2..‫ار‬‫و‬‫ﻟﻠﺪ‬ ‫اﻟﺬاﰐ‬ ‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﳏﻮر‬
3..‫اﻹﻃﺎر‬
4..‫اﳍﻴﻜﻞ‬
5..‫ار‬‫و‬‫اﻟﺪ‬
6..‫اﺋﻴﺔ‬‫ﻮ‬‫اﳍ‬ ‫اﻟﻔﺘﺤﺔ‬
7..‫ار‬‫و‬‫ﻟﻠﺪ‬ ‫اﻟﻌﻨﻔﻲ‬ ‫اﻹﻃﺎر‬
8.‫اﻹﻃﺎر‬ ‫ﳐﻤﺪ‬
9..‫ﻣﺆﺷﺮ‬
10..‫ﻣﺴﻄﺮة‬
11..‫اﻹﻇﻬﺎر‬ ‫ﻧﻈﺎم‬
12..‫ﻣﺮوﱐ‬ ‫ﻧﺎﺑﺾ‬

29. 28
:(‫اﻟﻤﻜﺎﻣﻞ‬ ‫)اﻟﺠﺎﻳﺮو‬ ‫اﻟﻤﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫ﺣﺴﺎس‬‫اﶈﻮر‬ ‫)ﻋﻠﻰ‬ ‫ﳏﻮرﺣﺴﺎﺳﻴﺘﻪ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫أﺿﻔﻨﺎ‬ ‫إذا‬Xً‫ا‬‫ﲣﻤﻴﺪ‬ (
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻣﺘﺤﺮك‬ ‫ﻣﻜﺎن‬ ‫ﻋﻠﻰ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻛﻨﺎ‬‫وﺗﺮ‬ .‫اﳉﲑﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﻧﺔ‬‫ز‬‫ا‬‫ﻮ‬‫ﳌ‬ ً‫ﺎ‬‫ﻟﺰﺟ‬Y‫ﻗﻴﻤﺘﻬﺎ‬θω‫اﳉﺎﻳﺮو‬ ‫ﻓﺈن‬
‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫ﺑﺎﻹﺳﱰﺷﺎد‬ ‫ﻳﺒﺪأ‬ ‫ﺳﻮف‬X‫اﳌﺮوﱐ‬ ‫اﻟﻌﺰم‬ ‫ﻣﻊ‬ ‫ازن‬‫ﻮ‬‫ﻳﺘ‬ ‫اﻟﺬي‬‫و‬ ‫ﺣﻮﻟﻪ‬ ‫اﳌﺘﺸﻜﻞ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﺑﺴﺒﺐ‬
‫اوﻳﺔ‬‫ﺰ‬‫ﺑ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻟﺬاﰐ‬ ‫اﶈﻮر‬ ‫ﻳﻨﺤﺮف‬ ‫ﻟﺬﻟﻚ‬ ‫ﻧﺘﻴﺠﺔ‬ .‫ﻟﻠﻨﺎﺑﺾ‬ϕ‫اﳌﺆﺛﺮة‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬θω.
) ‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬11‫ﺟﺴﺎﺳﻴﺘﻪ‬ ‫ﳏﻮر‬ ‫ﻋﻠﻰ‬ ‫ﻧﺎﺑﺾ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻣﻊ‬ ‫ﻳﺔ‬‫ﺮ‬‫اﳊ‬ ‫درﺟﺎت‬ ‫ﺛﻨﺎﺋﻲ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ (X.
‫اﻟﺸﻜﻞ‬9(‫اﳌﻜﺎﻣﻞ‬ ‫)اﳉﺎﻳﺮو‬ ‫اﳌﻄﻠﻘﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫ﺣﺴﺎس‬ :
:‫ﻳﻠﻲ‬ ‫ﳑﺎ‬ ‫اﳊﺴﺎس‬ ‫ﻳﺘﻜﻮن‬
1..‫ج‬‫ﻟﺰ‬ ‫ﳐﻤﺪ‬
2..‫اﻹﻃﺎر‬
3..‫اﳍﻴﻜﻞ‬

30. 29
4..‫ار‬‫و‬‫اﻟﺪ‬
5..‫ﻟﻺﻃﺎر‬ ‫ج‬‫اﳋﺮ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﻣﺒﲔ‬
:‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﺣﻞ‬‫ﺮ‬‫اﳌ‬ ‫وﻓﻖ‬ ‫اﳊﺴﺎس‬ ‫ﻳﻌﻤﻞ‬
1.‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﳊﺎﻣﻞ‬ ‫ان‬‫ر‬‫دو‬ ‫ﻋﻨﺪ‬Y‫ﻗﻴﻤﺘﻬﺎ‬θω‫ﺟﺎﻳﺮوﺳﻜﻮﰊ‬ ‫ﻋﺰم‬ ‫ﺳﻴﻈﻬﺮ‬GM‫ﻳﺘﻨﺎﺳﺐ‬‫ﻣﻊ‬
:‫اﳌﻌﺎدﻟﺔ‬ ‫وﻓﻖ‬ ‫اﳌﻘﺎﺳﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬
. . sin( ) .GM H Hθ θω ϕ ω= ≈
‫ﺣﻴﺚ‬ .‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﳌﺒﲔ‬ ‫اﻹﲡﺎﻩ‬ ‫ﰲ‬ ‫وذﻟﻚ‬H.‫ﻟﻠﺠﺎﻳﺮو‬ ‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﻟﻌﺰم‬
2.‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﻳﺆدي‬GM‫اﶈﻮر‬ ‫ﺣﻮل‬ ‫اوﻳﺔ‬‫ز‬ ‫وﺳﺮﻋﺔ‬ ‫اوي‬‫ز‬ ‫ع‬‫ﺗﺴﺎر‬ ‫ﻟﻈﻬﻮر‬X‫ﻗﻴﻤﺘﻬﺎ‬ϕ•
.
3.‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻇﻬﻮر‬ ‫ﻳﺆدي‬ϕ•
‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻫﺬﻩ‬ ‫ﻣﻊ‬ ‫ﻳﺘﻨﺎﺳﺐ‬ ‫اﳌﺨﻤﺪ‬ ‫ﰲ‬ ‫ج‬‫ﻟﺰ‬ ‫ﲣﻤﻴﺪي‬ ‫ﻋﺰم‬ ‫ﺗﺸﻜﻞ‬ ‫إﱃ‬
:‫وﻳﺴﺎوي‬
.DM D ϕ•
=
‫ﺣﻴﺚ‬ .‫اﳉﺎﻳﺮوﺳﻜﻮﰊ‬ ‫اﻟﻌﺰم‬ ‫ﳉﻬﺔ‬ ‫اﳌﻌﺎﻛﺲ‬‫و‬ ،‫ﺑﺎﻟﺸﻜﻞ‬ ‫اﳌﺒﲔ‬ ‫اﻹﲡﺎﻩ‬ ‫ﰲ‬ ‫وذﻟﻚ‬D.‫اﳌﺨﻤﺪ‬ ‫ﻟﺰوﺟﺔ‬ ‫ﺛﺎﺑﺖ‬
4.) ‫ج‬‫اﻟﻠﺰ‬ ‫اﳌﺨﻤﺪ‬ ‫ﻳﻌﻬﺎ‬‫ﺮ‬‫ﺗﺴ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻌﻤﻞ‬ ‫اﻟﱵ‬ ‫اﻟﻌﺎﺑﺮة‬ ‫اءات‬‫ﺮ‬‫اﻹﺟ‬ ‫ﲣﺎﻣﺪ‬ ‫ﻋﻨﺪ‬3:‫وﻳﺼﺒﺢ‬ ‫اﻟﻌﺰﻣﲔ‬ ‫ازن‬‫ﻮ‬‫ﺳﻴﺘ‬ (
. .
.
D G
H
D
M D M H θ
θ
ϕ ω
ϕ ω
•
•
= = = ⇒
=
:‫ﺑﺎﻟﺘﻜﺎﻣﻞ‬
.
H
D
ϕ θ= (1.9)
.‫اﳊﺎﻣﻞ‬ ‫ان‬‫ر‬‫دو‬ ‫اوﻳﺔ‬‫ز‬ ‫ﻣﻊ‬ ‫ﻣﺘﻨﺎﺳﺒﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫ﺣﺴﺎس‬ ‫ﻳﻘﻴﺴﻬﺎ‬ ‫اﻟﱵ‬‫و‬ ‫اﳌﺘﺸﻜﻠﺔ‬ ‫اوﻳﺔ‬‫ﺰ‬‫اﻟ‬ ‫أن‬ ‫أي‬
.‫ﻋﺰم‬ ‫وﻣﻮﻟﺪ‬ ‫وﻣﻀﺨﻢ‬ ‫اوﻳﺔ‬‫ز‬ ‫ﺣﺴﺎس‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ً‫ﺎ‬‫ﺑﺎﺋﻴ‬‫ﺮ‬‫ﻛﻬ‬‫أو‬ ً‫ﺎ‬‫ﻣﻴﻜﺎﻧﻴﻜﻴ‬ ‫اﳌﺨﻤﺪ‬ ‫ﻳﻜﻮن‬ ‫أن‬ ‫ﳝﻜﻦ‬
) ‫اﻟﺸﻜﻞ‬ ‫ﻳﺒﲔ‬12‫ﺑﲔ‬ ‫اﻟﻔﻀﺎء‬ ‫ﳝﻸ‬ ‫ﺣﻴﺚ‬ . ‫ﻋﺎﺋﻤﺔ‬ ‫ﻣﺴﺎﻧﺪ‬ ‫ذات‬ ‫وﺻﻠﺔ‬ ‫ﻳﺴﺘﺨﺪم‬ ‫ﻫﻨﺎ‬ ‫وﻫﻮ‬ ‫اﳌﻘﻴﺎس‬ ‫ﻫﺬا‬ ‫ﻣﺜﻞ‬ ‫ﻋﻠﻰ‬ ً‫ﻻ‬‫ﻣﺜﺎ‬ (
:‫اﻟﺘﺎﻟﻴﺔ‬ ‫ﺋﻴﺴﻴﺔ‬‫ﺮ‬‫اﻟ‬ ‫اء‬‫ﺰ‬‫اﻷﺟ‬ ‫ﻣﻦ‬ ‫ﻳﺘﻜﻮن‬ ‫وﻫﻮ‬ ‫ﺑﺎﻟﺴﺎﺋﻞ‬ ‫اﳍﻴﻜﻞ‬‫و‬ ‫اﻟﻌﺎﺋﻢ‬ ‫ان‬‫ر‬‫ﺟﺪ‬

31. 30
‫اﻟﺸﻜﻞ‬10‫اﻟﻌﺎﺋﻢ‬ ‫اﳌﻜﺎﻣﻞ‬ ‫اﳉﺎﻳﺮو‬ :
1..‫اﳍﻴﻜﻞ‬
2..‫ﻣﻌﺎﻳﺮة‬ ‫ﺻﺎﻣﻮﻟﺔ‬
3..‫ﻣﻌﺎﻳﺮة‬ ‫ﻛﺘﻠﺔ‬
4..‫اﻹﻃﺎر‬ ‫روﳌﺎن‬
5..‫اﻟﻌﺰم‬ ‫ﻣﻮﻟﺪ‬ ‫ار‬‫و‬‫د‬
6..‫اﻟﻌﺰم‬ ‫ﻣﻮﻟﺪ‬ ‫ﺛﺎﺑﺖ‬
7..‫اﻟﻌﺎﺋﻤﺔ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﺑﻴﺔ‬ ‫اﺠﻤﻟﻤﻮﻋﺔ‬ ‫ﻛﺄس‬
8..‫اﳉﺎﻳﺮﺳﻜﻮﰊ‬ ‫اﶈﺮك‬
9..‫ﲣﻤﻴﺪي‬ ‫ﺧﻠﻮص‬
10..‫اﻹﻃﺎر‬
11..‫اوﻳﺔ‬‫ز‬ ‫ﺣﺴﺎس‬
12..‫اﻹﻃﺎر‬ ‫روﳌﺎن‬

32. 31
‫ﺣﺴﺐ‬ ‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺼﻨﻴﻒ‬‫ﺣﺴﺐ‬ ‫اﻟﺠﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺼﻨﻴﻒ‬‫اﻟﻌﻤﻞ‬ ‫ﻣﺒﺪأ‬‫اﻟﻌﻤﻞ‬ ‫ﻣﺒﺪأ‬
‫اﻟﻔﺌﺎت‬ ‫ﰲ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﺼﻨﻴﻒ‬ ‫ﳝﻜﻦ‬ ‫اﳉﺎﻳﺮو‬ ‫ﻋﻤﻞ‬ ‫ﻣﺒﺪأ‬ ‫ﺣﺴﺐ‬‫ﺋﻴﺴﺔ‬‫ﺮ‬‫اﻟ‬:‫اﻟﺘﺎﻟﻴﺔ‬
1.‫اﳉﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫اﻹﻟﻜﱰوﻣﻴﻜﺎﻧﻴﻜﻲ‬‫اﻟﺘﻘﻠﻴﺪﻳﺔ‬ ‫ة‬
2.‫اﳉﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫ازي‬‫ﺰ‬‫اﻻﻫﺘ‬‫ة‬
3.‫اﳉﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫اﻟﻀﻮﺋﻲ‬‫ة‬
‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫ﺳﻜﻮﺑﺎت‬‫اﻹﻟﻜﺘﺮوﻣﻴﻜﺎﻧﻴﻜﻲ‬‫اﻹﻟﻜﺘﺮوﻣﻴﻜﺎﻧﻴﻜﻲ‬‫اﻟﺘﻘﻠﻴﺪﻳﺔ‬ ‫ة‬‫اﻟﺘﻘﻠﻴﺪﻳﺔ‬ ‫ة‬::‫ﻛﻲ‬‫اﳊﺮ‬ ‫اﳌﺨﻄﻂ‬ ‫ﺗﺘﺒﻊ‬ ‫اﻟﱵ‬ ‫اﳉﺎﻳﺮوﺳﻜﻮﺑﺎت‬ ‫ﺗﻠﻚ‬ ‫وﻫﻲ‬
:‫اع‬‫ﻮ‬‫أﻧ‬ ‫ﻋﺪة‬ ‫وﳍﺎ‬ ‫ﻛﺎردان‬‫وﺻﻠﺔ‬ ‫و‬ ‫ار‬‫و‬‫د‬ ‫ﺟﺴﻢ‬ ‫وﺟﻮد‬ ‫ﺣﻴﺚ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺠﺎﻳﺮو‬ ‫اﻟﺘﻘﻠﻴﺪي‬
‫اﳉﺎﻳﺮو‬‫اﻟﺘﻘﻠﻴﺪي‬.‫اﻹﺳﺘﻨﺎد‬
‫اﳉﺎﻳﺮو‬‫اﻟﻌﺎﺋﻤﺔ‬ ‫اﻟﻜﺎرداﻧﻴﺔ‬ ‫اﻟﻮﺻﻠﺔ‬ ‫ذو‬(‫اﻟﻌﺎﺋﻢ‬ ‫)اﳉﺎﻳﺮو‬.
‫اﳉﺎﻳﺮو‬.(‫ان‬‫ر‬‫اﻟﺪو‬ ‫ﻧﺘﻴﺠﺔ‬ ‫دﻳﻨﺎﻣﻴﻜﻴﺔ‬ ‫رﻓﻊ‬ ‫ﻗﻮة‬ ‫)ﲢﻘﻖ‬ ‫ار‬‫و‬‫ﻟﻠﺪ‬ ‫اﻟﺪﻳﻨﺎﻣﻴﻜﻴﺔ‬ ‫ﻳﺔ‬‫ز‬‫اﻟﻐﺎ‬ ‫اﳌﺴﺎﻧﺪ‬ ‫ذو‬
‫اﳉﺎﻳﺮو‬‫اﻟﻮﺻﻠﺔ‬ ‫ﻟﲑﻓﻊ‬ ‫ﺑﻀﻐﻂ‬ ‫اﻟﻐﺎز‬ ‫ﻳﺪﺧﻞ‬ ‫)ﺣﻴﺚ‬ ‫ﻛﺎردان‬‫ﻟﻮﺻﻠﺔ‬ ‫اﻟﺴﺘﺎﺗﻴﻜﻴﺔ‬ ‫ﻳﺔ‬‫ز‬‫اﻟﻐﺎ‬ ‫اﳌﺴﺎﻧﺪ‬ ‫ذو‬‫ﻋﻠﻰ‬
.‫ﻳﺔ‬‫ز‬‫ﻏﺎ‬ ‫وﺳﺎدة‬
‫اﳉﺎﻳﺮو‬.‫اﻟﻜﻬﺮﻃﻴﺴﻴﺔ‬ ‫اﳌﺴﺎﻧﺪ‬ ‫ذو‬
.‫اﻟﻜﺮوي‬ ‫ار‬‫و‬‫اﻟﺪ‬ ‫أو‬ ‫اﳌﻔﺼﻞ‬ ‫ذي‬ ‫اﳉﺎﻳﺮو‬ ‫أي‬ ‫اﻟﻜﺮوي‬ ‫اﳉﺎﻳﺮو‬
‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫ﺳﻜﻮﺑﺎت‬‫اﻻﻫﺘﺰازي‬‫اﻻﻫﺘﺰازي‬‫ة‬‫ة‬::‫ﻋﺪة‬ ‫وﳍﺎ‬ .‫ﻋﻤﻠﻬﺎ‬ ‫ﻣﺒﺪأ‬ ‫ﰲ‬ ‫أﺳﺎﺳﻴﺔ‬ ‫ﻛﻈﺎﻫﺮة‬‫از‬‫ﺰ‬‫اﻹﻫﺘ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﱵ‬ ‫ﺗﻠﻚ‬ ‫وﻫﻲ‬
:‫اع‬‫ﻮ‬‫أﻧ‬
.‫ازي‬‫ﺰ‬‫اﻻﻫﺘ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺣﺴﺎس‬
‫اﳉﺎﻳﺮو‬.‫اﻟﺘﻤﻮﺟﻲ‬ ‫اﻟﺼﻠﺐ‬
‫اﳉﺎﻳﺮو‬.‫ار‬‫و‬‫اﻟﺪ‬ ‫ذو‬ ‫ازي‬‫ﺰ‬‫اﻻﻫﺘ‬
‫اﳉﺎﻳﺮو‬.ً‫ﺎ‬‫دﻳﻨﺎﻣﻴﻜﻴ‬ ‫اﳌﻀﺒﻮط‬

33. 32
‫اﻟﺠﺎﻳﺮو‬‫اﻟﺠﺎﻳﺮو‬‫ﺳﻜﻮﺑﺎت‬‫ﺳﻜﻮﺑﺎت‬‫اﻟﻀﻮﺋﻲ‬‫اﻟﻀﻮﺋﻲ‬‫ة‬‫ة‬::‫ﺑﻌﺪم‬ ‫وﺗﺘﻤﻴﺰ‬ .‫ﻋﻤﻠﻬﺎ‬ ‫ﻣﺒﺪأ‬ ‫ﰲ‬ ‫أﺳﺎﺳﻴﺔ‬ ‫ﻛﻈﺎﻫﺮة‬‫اﻟﻀﻮء‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﱵ‬ ‫ﺗﻠﻚ‬ ‫وﻫﻲ‬
:‫اع‬‫ﻮ‬‫أﻧ‬ ‫ﻋﺪة‬ ‫وﳍﺎ‬ .‫ﻣﻬﺘﺰة‬ ‫أو‬ ‫ارة‬‫و‬‫د‬ ‫أﺟﺴﺎم‬ ‫وﺟﻮد‬
.‫اﻟﻠﻴﺰري‬‫و‬‫اﳉﺎﻳﺮ‬
.‫ﻳﺔ‬‫ﺮ‬‫اﻟﺒﺼ‬ ‫اﻷﻟﻴﺎف‬ ‫اﳉﺎﻳﺮوذو‬
‫اﻟﺠﺎﻳﺮوﺳﻜﻮب‬‫اﻟﺠﺎﻳﺮوﺳﻜﻮب‬‫اﻟﻤﻴﻜﺮو‬‫اﻟﻤﻴﻜﺮو‬‫اﻟﻜﺘﺮو‬‫اﻟﻜﺘﺮو‬‫ﻣﻴﻜﺎﻧﻴﻜﻲ‬‫ﻣﻴﻜﺎﻧﻴﻜﻲ‬‫)أو‬‫)أو‬‫اﻟﻤﻴﻜﺮوﻣﻴﻜﺎﻧﻴﻜﻲ‬‫اﻟﻤﻴﻜﺮوﻣﻴﻜﺎﻧﻴﻜﻲ‬((‫أن‬ ‫إﻻ‬ ‫ﻳﺔ‬‫ز‬‫ا‬‫ﺰ‬‫اﻹﻫﺘ‬ ‫اﳉﺎﻳﺮﺳﻜﻮﺑﺎت‬ ‫ﻣﻦ‬ ‫ﻧﻮع‬ ‫وﻫﻲ‬ :
‫اﺟﻬﺎ‬‫ر‬‫ﺑﺎد‬ ‫ﻳﺴﻤﺢ‬ ً‫ﺎ‬‫ﺧﺎﺻ‬ ً‫ﺎ‬‫ﻃﺎﺑﻌ‬ ‫ﳍﺎ‬ ‫ﺗﻌﻄﻲ‬ ‫اﳌﺎدة‬ ‫ﻣﻦ‬ ‫ﻗﻄﻌﺔ‬ ‫ﻣﻦ‬ ‫اﳉﺎﻳﺮو‬ ‫ﺗﻨﻔﻴﺬ‬ ‫ﻋﻠﻰ‬ ‫اﳌﻌﺘﻤﺪة‬ ‫اﻧﺘﺎﺟﻬﺎ‬‫و‬ ‫ﺗﺼﻨﻴﻌﻬﺎ‬ ‫ﺗﻘﻨﻴﺎت‬
.‫ﺧﺎﺻﺔ‬ ‫ﺑﺰﻣﺮة‬
.‫ﻋﺎﺟﻞ‬ ‫ﺑﺸﻜﻞ‬ ‫اﳉﲑﺳﻜﻮﺑﺎت‬ ‫اع‬‫ﻮ‬‫أﻧ‬ ‫ﺑﻌﺾ‬ ‫ﺳﻨﺪرس‬