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VectorCalculus

  

Torsion

  

compute the torsion of a curve in 3

 

Calling Sequence

Parameters

Description

Examples

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) command computes the torsion of the curve C, which must have exactly three components, that is, the curve that this Vector represents is in 3.

• 

The curve C can be specified as a free or position Vector or as a Vector valued procedure.  This determines the returned object type.

• 

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 which 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 two are not compatible, an error is raised.

Examples

withVectorCalculus:

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)

SetCoordinates'cylindrical'

cylindrical

(4)

simplifyTorsionⅇat,t,t,tassumingreal

ⅇ2at1+ⅇ2at

(5)

See Also

VectorCalculus

VectorCalculus[Binormal]

VectorCalculus[Curvature]

VectorCalculus[GetCoordinates]

VectorCalculus[PrincipalNormal]

VectorCalculus[RadiusOfCurvature]

VectorCalculus[SetCoordinates]

VectorCalculus[TangentVector]

VectorCalculus[TNBFrame]

VectorCalculus[Vector]