Coordinate system handedness

  • Thread starter 1MileCrash
  • Start date
  • #1
1,331
45

Main Question or Discussion Point

How do you define a right handed coordinate system for a basis which is not orthonormal?
 

Answers and Replies

  • #2
6,054
390
When you use the right hand rule and actually try to do that with your hand, you almost always get a non-orthonormal basis. If the angles between you fingers are very oblique, that is a good example; non of the angles may be zero, however.

More formally, it should be any three vectors not pairwise collinear, and forming a right-hand triad.
 
  • #3
1,331
45
Book just says scalar triple product positive for right hand, negative for left...
 
  • #4
6,054
390
Yeah, it boils down to that. One caveat is that it depends on the definition of the vector product, which itself includes right-handedness.
 
  • #5
1,331
45
That's interesting.. so really, if it is negative it means it "differs" from the way we have defined the vector product (right handed.)

Thanks.
 
  • #6
chiro
Science Advisor
4,790
131
It basically boils down to a positive determinant of the all the basis vectors in their natural order. If it's positive then it's right handed, if it's negative it's left handed (you can't get zero and if you do it means you've done something wrong).
 

Related Threads for: Coordinate system handedness

  • Last Post
Replies
3
Views
1K
Replies
12
Views
2K
Replies
3
Views
645
Replies
1
Views
1K
Replies
6
Views
729
Replies
6
Views
889
Replies
10
Views
1K
Replies
2
Views
7K
Top