TNB frame
In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle which moves along a continuous, differentiable curve in three-dimensional Euclidean space R3, or the geometric properties of the curve itself irrespective of any motion. More specifically, the formulas describe the derivatives of the so-called tangent, normal, and binormal unit vectors in terms of each other. The formulas are named after the two French mathematicians who independently discovered them: Jean Frédéric Frenet, in his thesis of 1847, and Joseph Alfred Serret in 1851. Vector notation and linear algebra currently used to write these formulas were not yet in use at the time of their discovery.
The tangent, normal, and binormal unit vectors, often called T, N, and B, or collectively the Frenet–Serret frame or TNB frame, together form an orthonormal basis spanning R3, and are defined as follows:
- 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
\begin{matrix}<br />
\frac{d\mathbf{T}}{ds} &=& & \kappa \mathbf{N} & \\<br />
&&&&\\<br />
\frac{d\mathbf{N}}{ds} &=& - \kappa \mathbf{T} & &+\, \tau \mathbf{B}\\<br />
&&&&\\<br />
\frac{d\mathbf{B}}{ds} &=& & -\tau \mathbf{N} &<br />
\end{matrix}
where d/ds is the derivative with respect to arclength, κ is the curvature and τ is the torsion of the curve. The two scalars κ and τ effectively define the curvature and torsion of a space curve. The associated collection, T, N, B, κ, and τ is called the Frenet–Serret apparatus. Intuitively, curvature measures the failure of a curve to be a straight line, while torsion measures the failure of a curve to be planar.

This is an excerpt from the article TNB frame from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article TNB frame at en.wikipedia.org was accessed 44 times in the last 30 days. (as of: 06/03/2014)
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Frenet–Serret formulas - Wikipedia, the free encyclopedia
[edit]. The Frenet-Serret frame moving along a helix in space. The Frenet–Serret frame consisting of the tangent T, ...
en.wikipedia.org/wiki/Frenet%E2%80%93Serret_formulas
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Mathlets: T-N-B Frame
How to use. Enter functions f (t), g(t), and h(t) in the text input fields marked "f (t)=", "g(t)=", and "h(t)=". (Example: f (t)=3cos t, g(t)=3sin t, h(t)=t/3); Click the "Graph" ...
cs.jsu.edu/~leathrum/Mathlets/tnbframe.html
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Tubes and the TNB frame - UNCA
In this course supplement, we'll learn about the TNB frame and how it can be used ... one way to do this but one particular elegant way is to use the TNB frame,  ...
facstaff.unca.edu/mcmcclur/class/Fall11CalcIII/handouts/TubesAndTNB.pdf
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Torsion and the Frenet Frame
Thus, B is a unit vector normal to the plane spanned by T and N at time t. The 3 vectors T, N, and B taken together are called either the TNB frame or the Frenet ...
math.etsu.edu/multicalc/prealpha/Chap1/Chap1-8/part4.htm
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CURVATURE, TORSION AND THE FRENET FRAME 1. Curvature In ...
CURVATURE, TORSION AND THE FRENET FRAME. 1. Curvature. In this section we are given a curve s ↦→ R(s) parametrized by arclength, i.e. the derivative ...
www.math.wisc.edu/~seeger/234/frenet.pdf
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Arc Length, Curvature and The TNB Frame
Arc Length, Curvature and The TNB frame. Introduction and Goals: The main goal of this lab will help you visualize the tools we use to describe the geometry of ...
facultyfp.salisbury.edu/despickler/personal/Resources/CalculusIII/MapleLabs/ArclengthTNB.pdf
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The Frenet Frame
Frenet frame (or Frenet Trihedron) Let a: I = (a,b) --> R3 be a curve parametrized by arc length s. To each value of the parameter s, we have associated three ...
www.math.hmc.edu/math142-01/mellon/Differential_Geometry/Geometry_of_curves/The_Frenet_Frame.html
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5: Motion and the TNB frame
Draft: Mon, 22 Mar 2010. 5: Motion and the TNB frame. Based on notes by Ben Woodruff. This learning module covers the following ideas. When you make your  ...
artsci.drake.edu/grout/lib/exe/fetch.php/courses/calculus_iii/spring_2010/07-motion.pdf
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Niggerfuxation and TNB - Niggermania…
General Forum of Niggermania ... Welcome to the Forums of Niggermania ! As a guest you have limited access to the forums and you can only post in the guest forum.
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TNB frame in science
Frenet–Serret formulas - Wikipedia, the free encyclopedia
The vectors in the Frenet–Serret frame are an orthonormal basis constructed by ..... Indiana University Technical Report; Iyer, B.R.; Vishveshwara, C.V. (1993), ...
[PDF]Unit Tangent and Unit Normal Vectors - it-educ.jmu.edu - James ...
Sep 19, 2012 ... Calculus III (James Madison University). Math 237 .... The Frenet frame is comprised of the three mutually perpendicular vectors T, N and B.
Mathlets - School of Mathematics - math.umn.edu - University of ...
3D Curvature Examples: Watch particles move along three-dimensional curves, including the TNB (Frenet) Frame and the osculating circle: helix; elliptical helix; ...
[PDF]DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces
University of Georgia ... Local Theory: Frenet Frame 10. 3. ..... Using Lemma 2.1 repeatedly, we now construct the Frenet frame of suitable regular curves.
Rational Frenet-Serret Curves and Rotation Minimizing Frames in ...
... and Aeronautical Engineering University of California-Davis California-Davis USA ... In our approach by using Frenet Seiret Frame we also specify the desired  ...
Three-Dimensional Graphing: The T-N-B Frame | Gateway to 21st ...
Three-Dimensional Graphing: The T-N-B Frame · Free · Curriculum support · Tool · Text/HTML ... Jacksonville State University. Show more properties. Keywords:.
[PDF]Parametric surfaces
University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell. 8. Frenet frames. Motivation: Given a curve T(v), we want to attach a smoothly ...
[PDF]Computing and approximating sweeping surfaces based on rotation ...
National University of Singapore, Singapore 0511. ABSTRACT ... The Frenet frame, extensively used in the graphics and CAD/CAM communities in de ning it1 ,2 ...
mth420 - Courses Template - University of Phoenix
Find tangent, normal, and binomial vectors (Frenet or TNB frame) for a given function. Describe motion along a curve using rectilinear and polar coordinates.
Books on the term TNB frame
Principles of Linear Algebra with Mathematica
Principles of Linear Algebra with Mathematica
Kenneth M. Shiskowski, Karl Frinkle, 2013
This means that any vector in 33 can be expressed as a linear combination of the unit vectors in the TNB frame. We will explore the concept of orthonormal bases in Chapter 8. The TNB frame is used, for example, in spacecraft navigation, ...
Principles of Linear Algebra with Mathematica (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs...
Principles of Linear Algebra with Mathematica (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs...
Ahmed I. Zayed, 2011
A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica®Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizin...
Scientia Magna, international book series, Vol. 5, No. 1
Scientia Magna, international book series, Vol. 5, No. 1
editor Zhang Wenpeng
Denote by {T, N, E) the moving Frenet frame along the curve cp in the space E±. For a space-like curve ip with first and second curvature, k and t in the space Ef , the following Frenet formulae are given in [4]. Let ip be a space-like curve with a ...
Calculus
Calculus
James Stewart, 2009
In general, the vectors T, N, and B, starting at the various points on a curve, form a set of orthogonal vectors, called the TNB frame, that moves along the curve as t varies. This TNB frame plays an important role in the branch of mathematics ...
Advances in Shannon's Sampling Theory
Advances in Shannon's Sampling Theory
Ahmed I. Zayed, 1993
Advances in Shannon's Sampling Theory provides an up-to-date discussion of sampling theory, emphasizing the interaction between sampling theory and other branches of mathematical analysis, including the theory of boundary-value problems, frames, wavelets, multiresolution analysis, special functions, and functional analysis. The author not only...
Multivariable Calculus
Multivariable Calculus
James Stewart, 2012
This frame plays an important role in the TNB t TNB BNT BNT N N B T T B SOLUTION We first compute the ingredients needed for the unit normal vector: rt sin ti cos tj k rt s2 1 branch of mathematics known as differential geometry and in its ...
Digital Watermarking: 6th International Workshop, IWDW 2007 Guangzhou, China, December 3-5, 2007, Proceedings...
Digital Watermarking: 6th International Workshop, IWDW 2007 Guangzhou, China, December 3-5, 2007, Proceedings...
2008
This book constitutes the refereed proceedings of the 6th International Workshop, IWDW 2007, held in Guangzhou, China, in December 2007. The 24 revised full papers together with 3 invited papers were carefully reviewed and selected from 81 submissions. The papers are organized in topical sections on watermark security; steganalysis; authentication;...
Calculus: Concepts and Contexts: Concepts and Contexts
Calculus: Concepts and Contexts: Concepts and Contexts
James Stewart, 2009
This frame plays an important role in the branch of mathematics known as differential geometry and in its applications to the motion of spacecraft. TNB t TNB BNT BNT N N B T T B FIGURE 7 x y z The Normal and Binormal Vectors At a given ...
Fluid Structure Interaction (Wit Transactions on the Built Environment)
Fluid Structure Interaction (Wit Transactions on the Built Environment)
2013
Containing papers presented at the Seventh International Conference on the topic, this book covers new developments in fluid structure interaction problems. First organised in 2001, the conference includes contributions from international experts on a variety of topics, including: Structure response to severe shock and blast; Hydrodynamic forces; A...
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Blog posts on the term
TNB frame
TNB Frames, Reflections, and Rogue AI | A New Music ~ Josh Parnell
joshparnell.com/blog/2012/08/28/tnb-frames-reflections-and-rogue-ai/
geometry - Different ways to work out the normal in the Frenet frame - Mathematics Stack Exchange
math.stackexchange.com/questions/277094/different-ways-to-work-out-the-normal-in-the-frenet-frame
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Family Day TNB 2013 Di FRIM Kepong ~ Glamorous MrJocko
Tahun ni ada peluang lagi sertai warga kerja wife untuk Family Day 1TNB bertempat di FRIM Kepong. Event sederhana, tetapi hampir 2,500 staff dan keluarga TNB KL Selatan berkumpul untuk Hari Keluarga 1TNB ini.
www.mrjocko.com/2013/10/family-day-tnb-2013-di-frim-kepong.html
TNB's Midseason Top 10 Nationals Prospects | Federal Reserve | Federal Reserve
As the season reaches its ceremonial halfway point, it’s a good time to take a look at the minor leagues and re-evaluate the team’s prospect situation. At the beginning of the season we often see several lists come out from various publications that rank each team’s top prospects, however we seldom see this list updated halfway through the year.
www.thenatsblog.com/federal-reserve/federal-reserve/tnbs-midseason-top-10-nationals-prospects.html
Spline Extrusions, Tubes and Knots of Sorts | kepo-ing Zz85
Posted on April 24, 2012 by Zz85.
www.lab4games.net/zz85/blog/2012/04/24/spline-extrusions-tubes-and-knots-of-sorts/
Wolfram Demonstrations Project
Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.
demonstrations.wolfram.com/CurvatureAndTorsion/
Living Tips For Malaysians: Don't Waste Money For TNB Power Breakdown
i-make-money-in-malaysia.blogspot.com/2009/10/dont-waste-money-for-tnb-power.html
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