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Math Q&A



Math Q&A
Differential Geometry
작성자 철인희수팔호
작성일 2007-09-07 (금) 23:49
분 류 diff geo
ㆍ추천: 0  ㆍ조회: 1007  
relation of orientation & direction
문제
Let a : I->R3 be a regular curve parametrized by arc length s.
Then k(s) is defined by |a''(s)|.
We can know that a'(s) and a''(s) are orthogonal, simply.
 
First, fix a vector a'(s1) where s1 is in I( the domain of a curve 'a').
It can be generated easily by assuming that a(s) is well-defined.
So does a''(s2), similarly.
 
I guess that the orientation of a curve 'a' is determined by the ordered basis of R3
Then, is the direction of a''(s) clockwise or counterclockwise for a'(s)?
Unless, is there no meaning in the orientation of R3?
Or, is it meaningless for Rsince there is infinitely many passes?
 
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relation of orientation & direction

참고문헌
Differential geometry of curves and surfaces (Manfredo P.Do Carmo/Sec1-5)
 
덧. matlab에 대한 질문을 위한 게시판이 하나 있었으면 합니다.
 
번호     글 제 목  작성자 작성일 조회
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5 diff geo 질문입니다. panzer 04-06 23:57 1121
4 diff geo    Re..질문입니다. augustine 04-07 09:05 1084
3 diff geo 교과서 연습문제 중 수정 augustine 03-26 10:07 1088
2 diff geo relation of orientation & direction 철인희수팔호 09-07 23:49 1007
1 diff geo    Re..relation of orientation & direction 1 augustine 09-08 18:10 963
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