compute the torsion of a curve in R^3 - Maple Help

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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 C, which must have exactly three components, that is, the curve that this Vector represents must be in 3.

• 

The curve C can be specified as a Vector or as a Vector-valued procedure. If C is a procedure, the returned object is a procedure. Otherwise, the returned object is an expression.

• 

If t is not specified, the function tries to determine a suitable variable name from the components of C.  To do this, it checks all of the indeterminates of type name in the components of C 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 C, C 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

withStudent[VectorCalculus]:

Torsionat+b,ct+d,et+f,t

0

(1)

simplifyTorsiont,t2,t3assumingt::real

39t4+9t2+1

(2)

Torsiont→cost,sint,t

t→122sint22sint2+2cost214+14sint2+14cost21+sint2+cost2+122cost22sint2+2cost214+14sint2+14cost21+sint2+cost2

(3)

SetCoordinatescylindrical

cylindricalr,θ,z

(4)

simplifyTorsionⅇat,t,t,tassumingreal

ⅇ2at1+ⅇ2at

(5)

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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