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Topic: Osculating circle

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	Encyclopedia :: encyclopedia : Circle (Site not responding. Last check: 2007-10-31)
		Usually however, the circumference means the length of the circle, and the interior of the circle is called a disk or disc.
		The circle centered at the origin with radius 1 is called the unit circle.
		All circles are similar; as a consequence, a circle's circumference and radius are proportional, as are its area and the square of its radius.
	www.hallencyclopedia.com /Circle (834 words)

	Osculating orbit - Wikipedia, the free encyclopedia
		In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space is the gravitational Keplerian orbit about a central body which best approximates the (more complex) motion of the object at a given instant in time.
		An osculating orbit and the object's position upon it are fully described by the six standard Keplerian orbital elements.
		To contrast the slowly changing osculating orbital elements to the proper orbital elements, which remain practically constant over timescales of millions of years.
	en.wikipedia.org /wiki/Osculating_orbit (211 words)

	Xah: Special Plane Curves: Nephroid
		Nephroid is the catacaustic of a circle with parallel rays.
		Nephroid is the envelope of a set of circles with centers on a base circle B and tangent to a fixed diameter of B. Proof.
		Base circle are not shown) Nephroid is the envelope of a diameter of the circle that generates a cardioid as an epicycloid.
	www.xahlee.org /SpecialPlaneCurves_dir/Nephroid_dir/nephroid.html (664 words)

	Curve
		Simple examples are the circle or the straight line.
		For example, a line segment can be traced out at different speeds, or a circle can be traversed a different number of times.
		One reason for the use of the Ptolemaic system of epicycle and deferent was the special status accorded to the circle as curve.
	www.brainyencyclopedia.com /encyclopedia/c/cu/curve.html (1350 words)

	Osculating Circle/Circle of Curvature (Site not responding. Last check: 2007-10-31)
		An osculating circle (circle of curvature) is a circle which is located on a curve.
		If the curvature is equal to a zero, the osculating circle does not exist at this point.
		Osculating circles: An osculating circle is represented in the bottom figure whose fill arc is the osculating point between the circle and an initial curve.
	www.mpi-sb.mpg.de /~shin/Research/CCurve/node5.html (97 words)

	Osculating, - Osculating polynomials
		The uniquely defined circle in the osculating plane of a curve g at s, Then the osculating sphere of g at s is the sphere that is a third order
		Osculating orbits are presented for 110 nearly parabolic comets.
		It lies in the osculating plane, tangent to the path, and it turns at the same rate as The radius of the osculating circle is the radius of curvature.
	www.findoutwebsite.com /?q=osculating (374 words)

	Comparison with osculating circle methods
		In such methods, a rim point P is reconstructed by estimating the osculating circle at P and its epipolar correspondents on the previous and the next rim.
		In such cases, the epipolar curves defined at P can not be considered as part of the same curve and methods based on the osculating circle lead to false solutions since they approximate both epipolar curves with a single planar curve: a circle (see for example figure 10).
		This shows that epipolar curves have to be estimated as two different curves and that a method based on the osculating circle allows only a partial reconstruction of the rim in the case of non-linear camera motions.
	homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/BOYER/node11.html (423 words)

	1-8.html
		In particular, the radius of the osculating circle is 1/
		and the center of the osculating circle is a distance of 1/kappa from the curve along the unit normal.
		Thus, the center of the osculating circle is the sum of the position vector
	faculty.etsu.edu /knisleyj/multicalc/Chap1/Chap1-8/1-82.html (348 words)

	Project Links \| Curvature Module (Site not responding. Last check: 2007-10-31)
		Since the curvature of a circle of radius R is the constant value 1/R, it is natural to use circles to help define curvature.
		The osculating circle is always tangent to the tangent line of the curve.
		At vertices the curve is either locally inside the osculating circle (at local maximums of curvature) or locally outside the osculating circle(at local minimums of curvature).
	links.math.rpi.edu /devmodules/curvature/html/osculating_concept.html (358 words)

	Radius of Curvature (Site not responding. Last check: 2007-10-31)
		The osculating circle is the circle that kisses the path.
		It lies in the osculating plane, tangent to the path, and it turns at the same rate as the path.
		The radius of the osculating circle is the radius of curvature.
	www.mathreference.com /ca-path,radius.html (408 words)

	The History of Curvature (Site not responding. Last check: 2007-10-31)
		In later times, this approximating circle would come to be known as the "circle of curvature" of a curve at a point; for the radius of the circle is inversely proportional to how much the curve bends at the point.
		The largest circle that is tangent to a curve (on its concave side) at a point has the same curvature as the curve at that point.
		In one of his works regarding curvature, Leibniz made the claim that an osculating circle has a four-point contact with a curve near the point for which the circle is drawn (Coolidge 377).
	www.brown.edu /Students/OHJC/hm4/k.htm (3531 words)

	Osculating Circles for Plane Curves (Site not responding. Last check: 2007-10-31)
		The word "osculate" means "to kiss." A succession of circles that converge to snuggly "kiss" a curve are said to be osculating circles.
		The tangent to a point on a curve was applied by the earliest investigators to study the derivative and thus Calculus.
		A minimum of three points on the curve are needed to determine, first the perpendicular bisectors, and then the center and radius of the osculating circle.
	curvebank.calstatela.edu /osculating/osculating.htm (367 words)

	Approximating circles and osculating circle (Site not responding. Last check: 2007-10-31)
		The green circle is the osculating circle at the white point.
		The light blue (cyan) circle is the circle through the white and the two fl points.
		When the fl points converge to the white one (use the player), this approximating circle converges to the osculating circle.
	www.math.aau.dk /~raussen/VIDIGEO/GEOLAB/appcurvcirc.html (65 words)

	curvature
		A measure of the amount by which a curve, a surface, or any other manifold deviates from a straight line, a plane, or a hyperplane (the multidimensional equivalent of a plane).
		For a plane curve, the curvature at a given point has a magnitude equal to one over the radius of an osculating circle (a circle that "kisses," or just touches, the curve at the given point) and is a vector pointing in the direction of that circle's center.
		The smaller the radius r of the osculating circle, the greater the magnitude of the curvature (1/r) will be.
	www.daviddarling.info /encyclopedia/C/curvature.html (430 words)

	Circle and Radius of Curvature
		, the center and radius of the osculating circle are given by the limits calculated in the preceding discussion.
		The abscissa of the circle of curvature is
		The ordinate of the circle of curvature is
	math.fullerton.edu /mathews/n2003/CurvatureMod.html (766 words)

	rov12_6.html
		The moving osculating circle of a plane curve (ellipse, logarithmic spiral, etc).
		F.1 denotes the unit tangent vector; F.3 - the osculating circle; F.2 - its radius as a line segment.
		F.5 denotes the osculating circle; F.4 denotes the segment of its position vector.
	math.haifa.ac.il /ROVENSKI/rovenski/rov12_6.html (455 words)

	Osculating Circle Maplet - Maple Application Center - Maplesoft
		This Maplet plots a parameterized space curve together with its osculating circle (the circle that best approximates the curve at the point of tangency) at a time t.
		The osculating circle lies in the plane determined by the tangent and normal to the curve, its radius is 1/curvature, and the line from the center of the circle to the point of tangency to the curve is parallel to the normal vector.
		The endpoints of the desired time interval are entered in the text boxes, and the time t when the osculating circle is computed is adjusted with the slider.
	www.maplesoft.com /applications/app_center_view.aspx?AID=1224 (180 words)

	Osculating - Osculating Infection (Site not responding. Last check: 2007-10-31)
		The light blue (cyan) circle is the circle
		English words defined with "osculating circle": Circle of curvature ♦; Osculating Expression using "osculating circle": osculating circle of a curve.
		A 22-year-old female graduate student at William and Mary College went to the infirmary complaining of a sore throat and difficulty
	infosvc.com /?q=osculating (190 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		Before hitting "Enter", # you will need to change the name "Pacific" to the name of the machine # you are using (e.g.
		Note that in the plane, the circle # of radius 1/scurvature # centered at [0, 1/scurvature] is given by # [(1/scurvature)cos(x), # (1/scurvature)(1+sin(x))].
		VCurvature is the curvature # vector.) # To move this circle to the osculating plane, we map [1,0] to the # tangent vector and [0,1] to # (1/scurvature))*VCurvature.
	www.math.cornell.edu /~henderson/books/dg/scripts/osculating_circle.txt (304 words)

	[No title]
		Construct the osculating circle of each of the four curves
		Show the trace of the osculating circle of each of the four curves
		Construct circles enveloping both the deltoid and the 3-cusped epicycloid
	oz.nthu.edu.tw /~u910204/GK008/GK002/GK002.htm (248 words)

	Body
		In this exercise, you can input a space curve and see the osculating circle, tangent, and curvature vectors at a given point.
		) and pick the point where we'll find the osculating circle by choosing a point in the domain.
		is the curvature vector.) To move this circle to the osculating plane, we map [1,0] to the tangent vector and [0,1] to
	www.math.cornell.edu /~henderson/books/dg/scripts/2-4b.html (142 words)

	javasketchpad (Site not responding. Last check: 2007-10-31)
		Circles Common Tangent to an Ellipse and a Circle
		Common Tangent Circle of Two Cardioids Sharing the Same Cusp
		Mutually Tangential Circles Each Tangent to a Same Fixed Circle at Fixed Point
	math2.math.nthu.edu.tw /jcchuan/java-sketchpad/jsp.html (185 words)

	topics
		An Invariant Property of Three Circle Meeting at a Point
		An Invariant Property of Three Mutually Tangential Circles
		Circle Common Tangent to a Circle and a Conic
	poncelet.math.nthu.edu.tw /disk3/cabrijava/outline.html (127 words)

	[No title]
		The red circle is "tangent to" the helix, i.e., it is an osculating circle for the helix at the point of contact.
		Put the mouse cursor inside the box below and the figure will rotate.
		This image was produced using Mathematica and converted to the animation with LiveGraphics3D
	www.lsus.edu /sc/math/rmabry/live3d/helix1.htm (59 words)

	3DCurve, TNB-Vectors, Planes and Osculating Circle - Maple Application Center - Maplesoft
		3DCurve, TNB-Vectors, Planes and Osculating Circle - Maple Application Center - Maplesoft
		The Maplet also plots the circle of curvature.
		The Maplets has been used as a tutorial in a Calculus III course.
	maplesoft.com /applications/app_center_view.aspx?AID=1603&P=mr200501 (77 words)

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