Search results
Results From The WOW.Com Content Network
On the example of a torus knot, the tangent vector T, the normal vector N, and the binormal vector B, along with the curvature κ(s), and the torsion τ(s) are displayed. At the peaks of the torsion function the rotation of the Frenet–Serret frame (T,N,B) around the tangent vector is clearly visible.
Geometric relevance: The torsion τ(s) measures the turnaround of the binormal vector. The larger the torsion is, the faster the binormal vector rotates around the axis given by the tangent vector (see graphical illustrations). In the animated figure the rotation of the binormal vector is clearly visible at the peaks of the torsion function.
A parametric C r-curve or a C r-parametrization is a vector-valued function: that is r-times continuously differentiable (that is, the component functions of γ are continuously differentiable), where , {}, and I is a non-empty interval of real numbers.
Several examples of adapted frames have already been considered. The first vector T of the Frenet–Serret frame (T, N, B) is tangent to a curve, and all three vectors are mutually orthonormal. Similarly, the Darboux frame on a surface is an orthonormal frame whose first two vectors are tangent to the surface.
Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.
This page was last edited on 3 June 2008, at 10:40 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply ...
Figure 4: The angular momentum vector L, the LRL vector A and Hamilton's vector, the binormal B, are mutually perpendicular; A and B point along the major and minor axes, respectively, of an elliptical orbit of the Kepler problem. An alternative conserved vector is the binormal vector B studied by William Rowan Hamilton, [16]
A normal vector of length one is called a unit normal vector. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by −1 results in the opposite vector , which may be used for indicating sides (e.g., interior or exterior).