Ad
related to: unit binormal vector calculator calculus problems pdf solutions
Search results
Results from the WOW.Com Content Network
T is the unit vector tangent to the curve, pointing in the direction of motion. N is the normal unit vector, the derivative of T with respect to the arclength parameter of the curve, divided by its length. B is the binormal unit vector, the cross product of T and N. The Frenet–Serret formulas are:
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.
Differentiable curve. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented ...
A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., where ‖ u ‖ is the norm (or length) of u. [1][2] The term normalized vector is sometimes used as a synonym for unit vector. A unit ...
Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the ...
Darboux frame. In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame as applied to surface geometry. A Darboux frame exists at any non- umbilic point of a surface embedded in Euclidean space. It is named after French mathematician Jean Gaston ...
Closed and exact differential forms. In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d ...
Direction cosine. In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three positive coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction.
Ad
related to: unit binormal vector calculator calculus problems pdf solutions