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Topic: Unit tangent vector

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	PlanetMath: derivation of unit vectors in curvilinear coordinates
		A tangent vector is a vector which is tangent to a coordinate curve formed by the intersection of the two coodinate surfaces.
		Most often we are interested in unit tangent vectors (a.k.a.
		This is version 7 of derivation of unit vectors in curvilinear coordinates, born on 2007-05-02, modified 2007-05-14.
	planetmath.org /encyclopedia/DerivationOfUnitVectorsInCurvilinearCoordinates.html (0 words)

	Frenet Trihedron
		The unit tangent vector u(t) is f'(t)i + g'(t)j + h'(t)k normalized so it is length 1.
		The unit principal normal vector is the normalized derivative of the unit tangent vector p(t) = u'(t)/
		The Frenet Trihedron is the vectors consisting of the unit tangent vector, unit principal normal vector, and unit binormal vector.
	www.math.byu.edu /~math302/content/learningmod/trihedron/trihedron.html (141 words)

	The Unit Tangent and the Unit Normal Vectors
		by as the unit vector in the direction of the velocity vector.
		Comparing this with the formula for the unit tangent vector, if we think of the unit tangent vector as a vector valued function, then the principal unit normal vector is the unit tangent vector of the unit tangent vector function.
		As you may guess the tangential component of acceleration is in the direction of the unit tangent vector and the normal component of acceleration is in the direction of the principal unit normal vector.
	www.ltcconline.net /greenl/courses/202/vectorFunctions/tannorm.htm (0 words)

	Calculus III (Math 2415) - 3-Dimensional Space - Tangent, Normal and Binormal Vectors
		While, the components of the unit tangent vector can be somewhat messy on occasion there are times when we will need to use the unit tangent vector instead of the tangent vector.
		The unit normal is orthogonal (or normal) to the unit tangent vector and hence to the curve as well.
		The binormal vector is orthogonal to both the tangent vector and the normal vector.
	tutorial.math.lamar.edu /AllBrowsers/2415/TangentNormalVectors.asp (528 words)

	135
		The unit tangent vector is the velocity vector divided by the speed.
		The normal vector is orthogonal to the tangent vector at the point of tangency.
		The osculating (kissing) circle to the curve is that circle tangent to the curve having a radius that is the radius of curvature.
	math.stcc.edu /CalculusIII/135.html (549 words)

	Vector (spatial) - Wikipedia, the free encyclopedia
		A spatial vector is a special case of a tensor and is also analogous to a four-vector in relativity (and is sometimes therefore called a three-vector in reference to the three spatial dimensions, although this term also has another meaning for p-vectors of differential geometry).
		Informally, a vector is a quantity characterized by a magnitude (in mathematics a number, in physics a number times a unit) and a direction, often represented graphically by an arrow.
		Vectors can be contrasted with scalar quantities such as distance, speed, energy, time, temperature, charge, power, work, and mass, which have magnitude, but no direction (they are invariant under coordinate rotations).
	en.wikipedia.org /wiki/Vector_(spatial) (3162 words)

	Normal Vector and Curvature
		The tangent line, binormal line and normal line are the three coordinate axes with positive directions given by the tangent vector, binormal vector and normal vector, respectively.
		Thus, the unit-length tangent vector is (-sin(u), cos(u), 0), the binormal vector is (0, 0, 1), and the normal vector is (-cos(u), sin(u), 0).
		Therefore, you are moving in the direction of the tangent vector, your "up" vector is in the direction of the binormal vector and the rate of turning and turning direction are given by the curvature and the direction of the normal vector, respectively.
	www.cs.mtu.edu /~shene/COURSES/cs3621/NOTES/curves/normal.html (890 words)

	physics - Vector (spatial)
		In physics and engineering, the word vector typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a "magnitude" and a "direction".
		A common example of a vector is force — it has a magnitude and an orientation in three dimensions (or however many spatial dimensions one has), and multiple forces sum according to the parallelogram law.
		In, we usually denote the unit vectors parallel to the x-, y- and z-axes by i, j and k respectively.
	www.physicsdaily.com /physics/Vector_(spatial) (1930 words)

	Osculating Circle
		That is, the curvature is the magnitude of the derivative of the unit tangent with respect to arc length.
		Note that the vector OC, the position vector for the center of the osculating circle, is the sum of the vectors OP and PC.
		The vector OP is the position vector r, while the vector PC points in the direction of the unit normal and has length equal to the reciprocal of the curvature.
	online.redwoods.edu /instruct/darnold/MULTCALC/osculating/osculating.htm (1499 words)

	12.4
		Since the velocity vector at time t points in the direction of motion, it must be tangent the the curve C traced by the vector valued function at time t.
		Sketch the graph and the unit tangent vector (!)
		Note that the unit tangent vector points in the direction of motion at time t, and N(t) is orthogonal to T(t) and points in the direction that the object is turning.
	www.ac.cc.md.us /~donr/CalcIII/unit2/lesson4/u2l4.html (680 words)

	Unit tangent, unit Normal
		The derivative of f at t points in the direction of the tangent line of the curve at f(t).
		A picture of the curve together with the tangent lines at, t=0, and t=1 is given by,
		The unit tangent vector to a curve at t=s is denoted by T(s).
	omega.albany.edu:8008 /calc3/vector-functions-dir/tangent-normal-m2h.html (0 words)

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