เนื้อหาบทที่ 4 : หัวข้อ 4.7[.pdf]

315 201 Physics of Matter
4 33
4.9 กก
4.11 ก m M
ก m M M >> m
M m M
m กก ก (Central Force) ก
กก กก …
…
F
=
Mm
− G ˆ
r
G
e
2 r
2
d r
dt
F = ma = m
2
∑
2
Mm d r
2
− G eˆ
r
= m = m( ɺɺ r − r ɺ θ ) eˆ
r
+ m( r ɺɺ θ + 2rɺ
ɺ θ ) eˆ
2
2
θ
(4.34)
r
dt
ก 4.16 ก 4.11 …
2
d r
2
dt
: ∵ r = reˆ
r
2
d r
2
dt
=
=
2
( ɺɺ r − r ɺ θ ) eˆ
+ ( r ɺɺ θ + 2rɺ
ɺ θ ) eˆ
θ
d
dt
dr
dt
r
=
dr
dt
d
dt
r
= ( reˆ
r
) = re ɺˆr
+ r = re ɺˆr
+ r ˆθ
d
dt
deˆ
dt
1×
dθ e
dt
⎛ deˆ
⎞ ⎡ d deˆ
r
θ ⎤
( re ɺˆ
+ r ɺ θeˆ
) = ⎜ɺɺ
reˆ
+ rɺ
⎟ + eˆ
( r ɺ θ ) + r ɺ θ ⎥ ⎦
r
⎡
⎛ 1×
dθ
⎞⎤
( ɺ r
eˆ
+ rɺ
ɺ θeˆ
) + eˆ
( rɺ
ɺ θ + r ɺ θ ) + r ɺ θ ⎜−
eˆ
⎟⎥ ⎦
=
r θ θ
r
⎢
⎣
( ɺ r − r ɺ θ ) eˆ
r
( rθ
2rθ
) 2 + ɺ + ɺ ɺ eˆ
θ
= ...
θ
⎝
⎝
r
dt
dt
⎠
⎠
⎢
⎣
θ
dt
dt
... .
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