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A plane curve with non-vanishing curvature has zero torsion at all points. Conversely, if the torsion of a regular curve with non-vanishing curvature is identically zero, then this curve belongs to a fixed plane. The curvature and the torsion of a helix are constant. Conversely, any space curve whose curvature and torsion are both constant and ...
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. That is, a regular curve with nonzero torsion must have nonzero curvature.
The torsion is a way to quantify this additional slipping and twisting while rolling a plane along a curve. Thus the torsion tensor can be intuitively understood by taking a small parallelogram circuit with sides given by vectors v and w, in a space and rolling the tangent space along each of the four sides of the parallelogram, marking the ...
A curve can be described, and thereby defined, by a pair of scalar fields: curvature and torsion , both of which depend on some parameter which parametrizes the curve but which can ideally be the arc length of the curve. From just the curvature and torsion, the vector fields for the tangent, normal, and binormal vectors can be derived using the ...
Download as PDF; Printable version; In other projects Appearance. move to sidebar hide. From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Torsion of ...
On November 25, Mercury goes retrograde in Sagittarius. Astrologer Donna Page explains how it will affect your zodiac sign—and how to head off the chaos.
In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative ...
Go to any sports game—whether it’s a high school game or a pro one—and you’re bound to see athletes on the sidelines drinking Gatorade. It’s likely a staple at your local gym too. A ...