compute the torsion of a curve in R^3

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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

(1)

(2)

proc (t) options operator, arrow; (1/2)*2^(1/2)*sin(t)^2/((2*sin(t)^2+2*cos(t)^2)^(1/2)*((1/4+(1/4)*sin(t)^2+(1/4)*cos(t)^2)*(1+sin(t)^2+cos(t)^2))^(1/2))+(1/2)*2^(1/2)*cos(t)^2/((2*sin(t)^2+2*cos(t)^2)^(1/2)*((1/4+(1/4)*sin(t)^2+(1/4)*cos(t)^2)*(1+sin(t)^2+cos(t)^2))^(1/2)) end proc

(3)

(4)

	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]