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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.
Here the vectors N, B and the torsion are not well defined. If the torsion is always zero then the curve will lie in a plane. A curve may have nonzero curvature and zero torsion. For example, the circle of radius R given by r(t) = (R cos t, R sin t, 0) in the z = 0 plane has zero torsion and curvature equal to 1/R. The converse, however, is false.
Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system. The intrinsic quantities used most often are arc length s {\displaystyle s} , tangential angle θ {\displaystyle \theta } , curvature κ {\displaystyle \kappa } or radius of curvature , and, for 3 ...
Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
Here are some of the basic properties and computations of Tor groups. [4]Tor R 0 (A, B) ≅ A ⊗ R B for any right R-module A and left R-module B.; Tor R i (A, B) = 0 for all i > 0 if either A or B is flat (for example, free) as an R-module.
The torsion tensor thus is related to, although distinct from, the torsion of a curve, as it appears in the Frenet–Serret formulas: the torsion of a connection measures a dislocation of a developed curve out of its plane, while the torsion of a curve is also a dislocation out of its osculating plane.
Far-right political pundit Nick Fuentes answers question during an interview with Agence France-Presse in Boston, Massachusetts, on May 9, 2016. 'Grateful to God that I am still alive'
For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: ΣH = 0 and ΣV = 0, and the torque a third equation: Στ = 0. That is, to solve statically determinate equilibrium problems in two-dimensions, three equations are used.
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