Curvature, Osculating Plane, and Tangent/Normal
- Author:
- Charles Reid, Ryan Hirst
The line perpendicular to the tangent, and lying in the osculating plane (the plane through "three consecutive points" on the curve), is called the Principal Normal. For example, this curve lies completely in the plane (it's 2D), so the principal normal will always lie flat on the worksheet.
The Unit Normal may be chosen to face either direction along this line. Here are two ways we might choose :
I'll use the first way; that is, I'll choose consistently as a right-handed coordinate system.
Note that, by continuous manipulation of this curve in 3 dimensions, I can still make appear -- from this point of view-- on the other side of (rotated by -90°). How?
And what physical meaning is implied?*
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*For example, try assigning the curve a left/right, and a top/bottom.