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Student[VectorCalculus][Torsion] - compute the torsion of a curve in R^3
Calling Sequence
Torsion(C, t)
Parameters
C
-
free or position Vector or Vector-valued procedure; specify the components of the curve
t
(optional) name; specify the parameter of the curve
Description
The Torsion(C, t) calling sequence computes the torsion of the curve , which must have exactly three components, that is, the curve that this Vector represents must be in .
The curve can be specified as a Vector or as a Vector-valued procedure. If is a procedure, the returned object is a procedure. Otherwise, the returned object is an expression.
If is not specified, the function tries to determine a suitable variable name from the components of . To do this, it checks all of the indeterminates of type name in the components of and removes the ones that are determined to be constants.
If the resulting set has a single entry, the single entry is the variable name. If it has more than one entry, an error is raised.
If a coordinate system attribute is specified on , is interpreted in this coordinate system. Otherwise, the curve is interpreted as a curve in the current default coordinate system. If the curve and the coordinate system are incompatible, an error is returned.
Examples
See Also
%1, %2, ... labels, Student[VectorCalculus], Student[VectorCalculus][Binormal], Student[VectorCalculus][Curvature], Student[VectorCalculus][GetCoordinates], Student[VectorCalculus][PrincipalNormal], Student[VectorCalculus][RadiusOfCurvature], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][TangentVector], Student[VectorCalculus][TNBFrame], Student[VectorCalculus][Vector]
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