# unit tangent

## unit tangent

[′yü·nət ′tan·jənt]
(mathematics)
A unit vector in the tangent plane at a point of a surface.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Denote by e(t) := [gamma](t) the unit tangent vector of [gamma](t).
In , the energy of a unit vector field X on a Riemannian manifold M is defined as the energy of the mapping X : M [right arrow] [T.sup.1] M, where the unit tangent bundle [T.sup.1] M is equipped with the restriction of the Sasaki metric on TM.
The tangent plane [T.sub.p]M, which contains the velocity vector [gamma]'([mathematical expression not reproducible]) of the initial geodesic [gamma] at P, can be decomposed into two independent (not necessarily orthonormal) unit tangent directions [mathematical expression not reproducible].
Next, we determine the unit tangent vector at the endpoints and subsequently calculate the corresponding tangent angle by using specified formula as indicated in the algorithm.
where ([d.sup.k], [[tau].sub.k]) is the unit tangent. When the path can be parameterized with respect to t, the step size h in the predictor step is usually referred to as [DELTA][t.sub.k]:
Since the curve [alpha](t) is also in space, there exists Frenet frame {T, N, B} at each points of the curve where T is unit tangent vector, N is principal normal vector and B is binormal vector, respectively.
We denote v as the arc-length parameter of f .We denote t(v) = f'(v)and we call t(v) a unit tangent vector of f at v.
which defines a unit tangent vector field on M and consider [e.sub.2] a unit vector field on M orthogonal to [e.sub.1] in such a way that {[e.sub.1], [e.sub.2] [zeta]} defines a positively oriented unit orthonormal basis for every point of M.
where [c.sub.u] is the effective air-drag coefficient, d is the yarn diameter, [v.sub.n] = v - (v x t)t is the normal component of the yam velocity (t is the unit tangent vector to the yarn at the given point).
Given a vector field v, the unit tangent vector t, the unit normal n, and the unit bi-normal b can be constructed as
For a unit tangent vector v [member of] UM, we denote by [[gamma].sub.v] the trajectory for a Kaahler magnetic field [B.sub.[kappa]] with initial condition [??](0) = v.

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