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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]
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].
In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral. If the floor projection is a logarithmic spiral , it is called conchospiral (from conch ).
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
The second generalized curvature χ 2 (t) is called torsion and measures the deviance of γ from being a plane curve. In other words, if the torsion is zero, the curve lies completely in the same osculating plane (there is only one osculating plane for every point t ).
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.
In statistical mechanics, the Zimm–Bragg model is a helix-coil transition model that describes helix-coil transitions of macromolecules, usually polymer chains. Most models provide a reasonable approximation of the fractional helicity of a given polypeptide; the Zimm–Bragg model differs by incorporating the ease of propagation (self-replication) with respect to nucleation.