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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 is called a general helix or cylindrical helix [4] if its tangent makes a constant angle with a fixed line in space. A curve is a general helix if and only if the ratio of curvature to torsion is constant. [5] A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space. [6]
Two helices (slinkies) in space. (a) A more compact helix with higher curvature and lower torsion. (b) A stretched out helix with slightly higher torsion but lower curvature. The sign of the torsion is determined by the right-handed or left-handed sense in which the helix twists around its central axis
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].
The torsion form, an alternative characterization of torsion, applies to the frame bundle FM of the manifold M. This principal bundle is equipped with a connection form ω , a gl ( n )-valued one-form which maps vertical vectors to the generators of the right action in gl ( n ) and equivariantly intertwines the right action of GL( n ) on the ...
The normal curvature, k n, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, k g, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τ r, measures the rate of change of the surface ...
A helix piercing is the upper cartilage inclusive of everything between the earlobe and the top of the ear curve. Here is a guide to helix facts and aftercare.
Torsion of a curve; Tortuosity; Total curvature; Transcendental curve; Triple helix; Trisectrix; Truncus (mathematics) V. Variation diminishing property; Vertex (curve)