Let be an interval and let be a parameterized space curve, assumed to be regular (http://planetmath.org/SpaceCurve) and free of points of inflection. We interpret as the trajectory of a particle moving through 3-dimensional space. The moving trihedron (also known as the Frenet frame, the Frenet trihedron, the repère mobile, and the moving frame) is an orthonormal basis of 3-vectors defined and named as follows:
|the unit tangent;|
|the unit normal;|
|the unit binormal.|
A straightforward application of the chain rule shows that these definitions are covariant with respect to reparameterizations. Hence, the above three vectors should be conceived as being attached to the point of the oriented space curve, rather than being functions of the parameter .
Corresponding to the above vectors are 3 planes, passing through each point of the space curve. The osculating plane at the point is the plane spanned by and ; the normal plane at is the plane spanned by and ; the rectifying plane at is the plane spanned by and .
|Date of creation||2013-03-22 12:15:44|
|Last modified on||2013-03-22 12:15:44|
|Last modified by||rmilson (146)|