What do you mean by torsion in mathematics?

In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the plane of curvature. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve.

What is curvature and torsion?

Curvature: Motion in several dimension has two aspects: one is its speed of motion; the other the shape of the curve it follows. The plane of motion is that normal to a v. The torsion of the curve is the magnitude of the rate of change of a unit vector in the direction of a v with distance along the curve.

What is the physical meaning of torsion?

A force that twists something is called torsion. In physics, you can calculate torsion using a formula. The turning or twisting force that causes torsion is called torque.

What is torsion example?

To turn on a gas, a burner knob is rotated. This rotation occurs when a twist or torsion force is applied by the person. Many other kitchen appliances make use of the similar twist force for their respective operations. For example, turning on the knob of a mixer grinder, increasing time period of a microwave, etc.

What is torsion engineering?

Torsion refers to the twisting of a structural member that is loaded by couples (torque) that produce rotation about the member’s longitudinal axis. In other words, the member is loaded in such a way that the stress resultant is a couple about the longitudinal axis and the response is a twisting motion about that axis.

Is torsion a vector or scalar?

Antisymmetric torsion in four dimensions acts like a vector. If it constitutes a universal background effect built into spacetime, then it violates the equivalence principle.

Is torsion and torque the same?

Torque and torsion are both related to turning effects experienced by a body. The main difference between torque and torsion is that torque describes something that is capable of producing an angular acceleration, whereas torsion describes the twist formed in a body due to a torque.

What is a torsion in engineering?

What is torsion load?

A torsion force is a load that is a applied to a material through torque. The torque that is applied creates a shear stress. If a torsion force is large enough, it can cause a material to undergo a twisting motion during elastic and plastic deformation.

What is math curvature?

curvature, in mathematics, the rate of change of direction of a curve with respect to distance along the curve.

What is meant by torsion in Algebra?

Torsion (algebra) In abstract algebra, torsion refers to the elements of finite order in a group and the elements annihilated by any regular element of a ring in a module.

What is the torsion of a planar curve?

The torsion of a space curve, sometimes also called the “second curvature” (Kreyszig 1991, p. 47), is the rate of change of the curve’s osculating plane. The torsion is positive for a right-handed curve, and negative for a left-handed curve. A curve with curvature is planar iff. The torsion can be defined by

What is a torsion element in ring theory?

In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements.

What is the significance of torsion in topology?

The relevance of this notion to topology comes from torsion in the Fundamental group or Homology (mathematics) groups of a space, which roughly indicates that the space has some interesting “twisting” in it.