??????? 1??E2???

1
????????? ??????? 1??E2???
?? ?? ?? ??
2
members
????(????????) ????????????????Max Plank
Institute???????? ????
????(???????) ???????????????????? ?????? ????
3
members
TA ???????????? 11257088????? 11257040 ???? 1125
7090 ???? 11257047 ???? 11257032 ????
4
Introduction
1.??? ??????? ??
(???????????) ?????????
ISBN978-4781910970
2.???????????????????? 1)http//www.tuat.ac.jp/s
ameken/ 2)????????????????? 3)2014? ???????
(1????) ???????? (ppt)?????
5
Introduction
3.????????????????????????? 1)
http//www.tuat.ac.jp/gakusyu/ 2)???? ?? ??
?????
6
Introduction
4.????
5.???? ???? S100?90,A89?80,B79?70,C69?60, D5
9?0 S?C?????????E1????????? ??30? ??20? ????????
50?
7
Introduction
6.???????????????
7.?????????
?????????????????3?????
???????????????????????????????
????????(?????13?????????) ??????????
8
Introduction
??? ???????4??????????? ????????? ?? ???????????
????????? ?????
9
1. ??????(1)
1.1 ?????? 1.2 ?????????? 1.3 ????????????? 1.4
??????????
10
???????????
??6???t0????????? ?x?????????????????
????? 1.????????????? 2.??????????? 3.???????????
????????
11
1.1 ??????
??m???P???r?????????(???????)????????????? ?????
???????????????????? ????????????????? ???? ???
?????
12
1.1 ??????
???????????????35.699o,??139.158o????????????????
???????????????????????????????6378.137km????
13
1.2 ??????????
P??X-Y????????????Q???? OX?OQ???????OZ?OP?????f? O
P????r????? ?????? ???????????????
?????????
14
1.2 ??????????
???????? 2???????? f???90?? ???X-Y???????
???? ??????????????35.699o,??139.158o????
?????????????????????????????? ????
15
1.2 ??????????
X-Y??????a????????????? ??????????
16
1.3 ?????????????
??P????????????????? ????????????????? ???????????
?? ??P???????P????????? ?????(??????????)
17
1.3 ?????????????
????????????????? ?????????? ????????
? X-Y??????r???????0???????????????????????? ?0?
??????????????????
18
1.3 ?????????????
??????? ????? ???????????????
19
1.3 ?????????????
?????????2??????????? ?????????????? ???????
20
1.4 ??????????
1.????????????? 2.????????????
3.????2????
1)??(inner product, scalar product)
????????????
21
1.4 ??????????
2)??(outer product, vector product)
????x????????
???XYZ???YZ?ZX?XY??????? ????????????
22
1.4 ??????????
???????
?????????????? ???????????????
23
1.4 ??????????
?????? ?????? ???????
24
?????????
????????????trigonometric function???????
????Multiplication rule
????Power rule ????ordinary
differential equation
a, b ????????????
Euler's formula
25
?????????
???
????????
26
?????????
???? ???????
27
2.??????(2)
2.1 ?? 2.2 ?? 2.3 ??? 2.4 ?????? 2.5 ?????
28
2.?????????
???????
?????????????? ???????????????
29
2.?????????
?????? ?????? ???????
30
2.?????????
?? ?? ???????
31
2.4. ??????
?????? ???????????????????????? ??????????? ???
??? ??????? ???????????????????????????? ?????
???????????????????????????
32
2.5. ?????
? ??r????????????????m? ?????????????

?????? ?????????????????? ?????????????????? ????
????????? ??????????????????????? ???????????

33
2.5. ?????

34
2.5. ?????

??T
35
3. ????
3.1 ?????????? 3.2 ?????????? 3.3 ?????????? 3.4
??????
36
3. ????
? x???????B??????????????????y?????v???????? (1
)????B,?????v?????????? (2)???? ?????
??????????? (1) ????????q????????
????????(1)????????????????????????????
37
3. ????
38
3. ???3??
1.????? 2.????? 3.????????(??????) Law of
action and reaction (Principle of Momentum
Conservation) ?.??3?????????????????
the principle of inertia
Equation of motion
39
3. ???3??
??? ??????????????? ???????????????????
??? ???? ???????????? ????????????????
40
3. ???3??
????m?????????? ?????Fgmg??????? ???????????????
??????????????N ???????????????? ??????????? ???
???????????? ????????????????????? ???????????????
???????? ????????????????
41
3. ???3??
10339.29
? ??1?????????? 101325 Pa(N/m2)???? ?????g?9.806
m/s2???? ????????????? ??1m2???????????
??
??
TA1
42
3. ???3??
??????????m??? ??????????? ????????? ?F???????R???
????????????? ????????????????????????N????? ?
???
43
3. ???3??
?????????????? ???R????(??????? ??)??????????? ??
?????????????? ??????????????? ???????????
????? ?????????????
44
3. ???3??
?????????? ???? ?????????????????????? ?
????????
45
3. ???3??
? ????m??????v???? ????? ????????? ???????????????
??? ???????????????? ? ????m???????? ??k?????????
????? ????????????????? ?????????? ???????????????
??
TA2
TA3
46
3. ???3??
???M????????????????m????????? ??????????????????
??????????????????????????? ????????????? ????????
?????? ????????
TA4
47
??????
???? ??? x??? ????? ???????
???? ?????
mr2?
48
3. ???3??
? ??M?m???????? ??k?????????????? ????????????????
? ??????? ???????? ????????????Reduced
mass Mgtgtm????? M1.5m?????

TA5
49
3. ???3??
??????????????????????M??????m???????????????????
???????????????????????? ????????????? ?????????
TA1
50
4.???????(1)
4.1 ???? 4.2 ???? 4.3 ???? 4.4 ???
51
4.???????(1)
????????????????? ?????????? ??????????????t????
?????????????? ?????????????????????????????????
??????????
52
4.???????(1)
????p(px,0,0)????F(0,0,Fz)??? t???? p(px,0,
Fzt)???? ?p(0,0, Fzt)???? ???
??? ??????????px??????? ????
????????????????????
53
4.1 ????parabolic movement
v0??????m????????????????? ???? ??? ???
y
?
x
54
4.1 ????parabolic movement
???????????? ??????(???????)?????? ??????t?
?????????????? ?????t2?????????????? ??????????t?
??t2?????????????
55
4.1 ????parabolic movement
??????????t??t2????????t0????
???? ???? ???t0???????????t0???
?????????????
56
4.1 ????parabolic movement
t0???????????r0? X????????????r1?
????????????r2?
57
4.2 ????
?????????t0?z0?z????? -v0?????m???????????? ???
??? ?????
????
58
4.2 ????
?????????t0?z0?z????? -v0?????m???????????? ???
??? ?????
????? 1.????????????? 2.??????????? 3.??????????
?????????
????
59
4.2 ????
????
????
??????????? ?????? ????? v?
60
4.2 ????
v?t0?-v0???? ???v? ???z?
61
4.2 ????
?-v00???????????tltlt????? ????????????? -v0??
??????????????
TA5
62
4.2 ????
?-v00???????????tltlt?????
63
4.2 ????
????????????v ???z ??????????????? ?????C?0
??????????????????????????????
TA4
64
4.2 ????
65
4.2 ????
??????
?????? Pa?s ???? ????
66
4.2 ????
?-Z ????????????????????m ??????v ????????v??v 2
????????F -Cv D v 2 ????????????????????????????
???????
67
4.2 ????
C?0?? ???? D?0?? ????
TA1
68
???????E2 ??????? ??????? 2008?12?18?(?)
?1. ??Q??????????????????????????????0.5m?10m????
??????Q??????g (1 m/s2)?????????(???C(50
Nsm-1))??????0.5 m?10 m???????????????????????????
?????????????????????????????50kg???? ?10.5s,
1.0s, 1.5s, 2.0s, 2.5s, 3.0s, 3.5s, 4.0s, 4.5s,
5.0s, 5.5s, 6.0s, 6.5s, 7.0s, 7.5s, 8.0s, 8.5s,
9.0s, 9.5s, 10.0s
TA2
69
????????
????????????????????? ???m???????t???????????E?
???????? ?????x???t0??????????????????? ?????????
????????????????? ? ???????????????????
????? ?????????????t????????????
70
????????
??? ??????????? ???????? ?????????????t?????
????????t???????????????????? ????????????? ????
?????????????
71
????????
?????S???????I? ????????????????L??????VEL ????
?? ??????????? ????????????? ??
????????????? ?? ????????????? ???
????
72
????????
TA3??????????????? ?????????????? TA4????????
???????????? ???E???????? TA3
???????V???L???????? ?????????????? ??????
???L???????? TA4 ??????????50nm??? T
A3 ??????????? TA4
?????????0.5V??? TA3 ?????????1.0x107 V/m??????
?????
73
????????
TA4 ?????t?m?????????? TA3 ???? t1x10-13 s,
m3x10-31 kg ?????? TA4 ??????????? TA3
?????????????? TA4 ?????????? TA3 530
km/s!!???????????????????? ??!
????????????1???????? ?????????????????????
74
4.3 ????
TA5??1m/s?????????? TA5?????59 kg???? ??????5.9x10
24 kg???? ?????????????? ???TA5???????????????????
?????????????? TA5???????????? ??????????????????
?

75
??????? ??????? ?????2005?7?1?(?)
???????m??????v0???a??????????????????????????????
??µ??????????x?????????????????0??????????????????
????????????????-??????m, g,(?????),
v0,a,µ????????????????
76
??????? ??????? ?????2005?7?1?(?)
????????????????(?)???????x????????(?)????????????
t???????(?)??????????0????????????????????(?)?????
???????????????????(?)????????????????????????(?)?
????????????????x????????(?)????????????????????0?
??????????????????(?)?????????????(?)???? ????????
??????? ??0????????????0 ???????????????? ???(?)??
??
77
??????? ??????? ?????2005?7?1?(?)
78
4.3 ????
???????v0???????? ???????????????? ???????????? 1)
??????? ?????? (1)

??????????????????????? Yes,????(1)??????????????
??? ???????????? (2) ????


79
4.3 ????
??t????????
(3) ??t???????????E??

80
4.3 ????
??t???????????????U?? ???? ???????E??????
??????U?????????
81
4.3 ????
(2)??????????????µ???????????
???????????????? ??????????????
82
4.3 ????
???????? x???????????? ????????????????????????
??????????????????????????????
83
4.3 ????
????????????? ????????x0???? ??v0?????????? ?????
xx0??????????? ???????????????v0??????????? ??t
???x???????????????????? ???? ?? ??
(1) (2)
84
4.3 ????
?? ?? ?? ???? ?? ?? ?? ????
(3) (4) (5) (6) (7) (8)
85
4.3 ????
???????????? ???????
??? ???? ??? ????
(4) (5) (7) (8)
86
4.3 ????
????????????????????????? ??????? ????? ??????
???? ???????????????? ?????????? ?????? ?????????
87
4.3 ????
????????????????????T??????????????????????? ???
???????????????????????????????????? ?????????
??????????????????
88
4.3 ????
??????????????? ????????? ??????????? ????? ???
??? ????
?
mg
89
4.3 ????
????????????? ????0??????0????
?
mg
90
4.3 ????
91
4.3 ????
????????????H?????? ?????
???????? ???????????????H??????????????????????
???
?
mg
92
4.3 ????
??????????????? ????? ???g9.8,
l1????????2???????
93
4.3 ????
???? ?????????? ????????
?
mg
94
4.3 ????
???? , g9.8, l1????
???? ????????
?
mg
95
4.3 ????
1???2.16 s???? ?????ltlt? ?????
????????(??)
?
mg
96
4.3 ????
???????? ????????H0.5, g9.8, l1 ????2.16
s???? ???????ltlt?????? ???????????2.01
s???? ???ltlt??????????????????
?
mg
TA1
97
4.3 ???
P7610 ?0????????????? ??????? ???? ???
? ????
98
4.3 ???
?0?????????????
99
4.3 ???
???X-Y????????r????????????????m????????? ???????
?????? ???????? ?????? ????????
100
4.3 ???
???? ???????????????????? ???? ??????????????
???? ?????????????????? ???????????????
?????????????? ???????????????????
101
4.3 ???
????X????????????? ?????????????????????
??????? ??? ?????
102
4.3 ???
???????
???????????????
????????????????????????????????????????(????)????
???????????????k???m ??????????????????? ?????? ?
??????a?????????????????????????????
103
4.3 ???
?????????????m??????????
(1)
???? ????? (?)
(?)
(?)
???????(1)?????.
104
4.3 ???
? ?????????????????m??????????
(1)
?????? ?????
????????????????
????????? (?)t0?xa,v0 (?)t0?x0,vv0 (?)t0?x
a,vv0????a,v0gt0
105
4.3 ???
? ???????????????????????m??????????
???????????????? ?????t0?x0,vv0????????????
106
5.???????
5.1 ??????????????? 5.2 ???? 5.3 ????
107
5.2 ????
???????????????? ?????????????? ????????????? ?
? ?????????????????? ?????????????????????? ??????
???????????????????????????????-???????????? ????
?????????????????????????????????????????????????-
?????????
108
5.2 ????
?????????????????? ???????? ????k,
??????a? ????????????? ????????????????? ????????
??????????????????
109
5.2 ????
???? ?? ?????? ??? ????
110
5.2 ????
???? ??? ???????????????? ?????
????????? ????
111
5.2 ????
??? ? ???? ????
112
5.2 ????
?????????? X0???t0?? X0????????? ??????????
??????????? ????????????????
113
5.2 ????
???? ????????????? ?????
114
5.2 ????
?????????????????
??
??
??(s)
115
5.2 ????
?????????????????
??????????????
??????????????
??
??(s)
??
116
5.2 ????
??????????????
??
??
??(s)
117
5.2 ????
??????????????
?????????????????????????????????????????????????
??
??(s)
??
118
5.2 ????
??? ?????????? ?????????????
119
5.2 ????
??????????????????????ß?????????????????????
???????????????????????
120
5.2 ????
?????????????????????????????????????????ß????????
????????????????????????????????????????
121
5.2 ????
??? ?????????? ??? ??????????????????
????????
122
5.2 ????
???t0?0???? ??????????????????????????
??
123
5.2 ????
?????????????????????ß????????????????????????????
?????ß?????????????????????????????
124
5.2 ????
????b????????tb??? ???? x?????????????b???
? ????????????????? ?????? ?05,
ß20?????????1.6 s ???????? ?05?1/4???0.31
s????????? ß20????????????????????????????
125
5.2 ????????
???? t0?v0???? ????? ????? ????
126
5.2 ????????
LCR???? ?? ??????????????????????????
127
5.2 ????????
LCR???? ?? ??????
??????????????? ??????????????
128
5.2 ????????
? L1 mH, C1 µF R10O??? ????2?????? ?
??????RC??????? L1 mH, C1 µF?R10KO???
????
3.12E04
TA1
TA2
129
5.3 ????
F
??????????????? ???????????? ?????
130
5.3 ????
F
???
131
5.3 ????
F
??????0???????????????????????????????? ??????????
????????????????????????????????? ?????ß??????????
???????
132
5.3 ????
F
??ß????????????????? Q??????Q?????????????????
133
5.3 ????
LCR?????? ?????? R????????????????
134
5.3 ????
??????0??????????? ?????????????? ?????????????? ?
????????????????? ? ?????????????????????????????
????????
F
TA3?4,5
135
5 ????
2????m????????k1,k2???????????????????? N??
???1?2????????2?????????????????????????????
136
5 ????
??????? ??????? ???????k1???????????????2
m???2k2???????????????????????????x1, x2?
137
5 ????
??????? k1???????????????
???? ??????????????????????? ????????
138
5 ????
?????
139
5 ????
????????1?2??????????????x1,x2?????
??????? X x1x2, Y x1-x2
??????????????
x1
x2
140
5 ????
X??Y????? ? ???????????? ???
??
??????????????????????2???????????????!