Search results
Results from the WOW.Com Content Network
The Frenet–Serret formulas were generalized to higher-dimensional Euclidean spaces by Camille Jordan in 1874.. Suppose that r(s) is a smooth curve in , and that the first n derivatives of r are linearly independent. [2]
The Frenet–Serret formulas are a set of ordinary differential equations of first order. The solution is the set of Frenet vectors describing the curve specified by the generalized curvature functions χ i .
The Frenet–Serret formulas show that there is a pair of functions defined on the curve, the torsion and curvature, which are obtained by differentiating the frame, and which describe completely how the frame evolves in time along the curve. A key feature of the general method is that a preferred moving frame, provided it can be found, gives a ...
Jean Frédéric Frenet (French:; 7 February 1816 – 12 June 1900) was a French mathematician, astronomer, and meteorologist. He was born and died in Périgueux , France. He is best known for being an independent co-discoverer of the Frenet–Serret formulas .
3.10 Formulas and other tools. 3.11 Related structures. 4 Lie groups. ... Frenet–Serret formulas; Curves in differential geometry; Line element; Curvature; Radius ...
Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors
In the case of the Frenet–Serret frame, the structural equations are precisely the Frenet–Serret formulas, and these serve to classify curves completely up to Euclidean motions. The general case is analogous: the structural equations for an adapted system of frames classifies arbitrary embedded submanifolds up to a Euclidean motion.
A space curve, Frenet–Serret frame, and the osculating plane (spanned by T and N). In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point.