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XYYX ''''''  XYYX ''''''  XYYX ''''''  (X (s),Y (s),0) 

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預備知識: τ=

(X (s),Y (s),0) 

τ´=(X〞,Y〞, 0)

⇒τ·τ=1

⇒τ·τ´=0 ∴τ⊥τ´

τ×τ´=

( ' ''X Y Y X k' '')

 ×' 

( ')

X 2

 ( ')

Y 2

( '')

X 2

 ( '')

Y 2

·1=

X Y' ''Y X' ''

=1·

( '')X 2( '')Y 2

·1=

X Y' ''Y X' ''

故得證:

( '')X 2( '')Y 2

=

X Y' ''Y X' ''

2012/3/28 2012 工數(二) 向量微積分 作業 2-曲率半徑解答(許哲崙).doc 許哲崙 製

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