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VectorCalculus

  

Curvature

  

compute the curvature of a curve

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Curvature(C, t)

Parameters

C

-

free or position Vector or a Vector valued procedure; specify the components of the curve

t

-

(optional) name; specify the parameter of the curve

Description

• 

The Curvature(C, t) command computes the curvature of the curve C.

• 

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

• 

If t is not specified, the function tries to determine a suitable variable name by using 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, that 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, it 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:

Curvaturecost,sint,t,t

142cost2+2sint22

(1)

CurvaturePositionVectorcost,sint

sint2+cost2

(2)

cCurvaturet→t,t2,t3:

simplifyctassumingt::real

29t4+9t2+19t4+4t2+13/2

(3)

Curvatureacost,asint,tassuminga::constant

a2cost2a2+1+a2sint2a2+1a2+1

(4)

SetCoordinates'polar'

polar

(5)

simplifyCurvatureⅇt,tassumingt::real

122ⅇt

(6)

See Also

assuming

VectorCalculus

VectorCalculus[Binormal]

VectorCalculus[GetCoordinates]

VectorCalculus[PrincipalNormal]

VectorCalculus[RadiusOfCurvature]

VectorCalculus[SetCoordinates]

VectorCalculus[TangentVector]

VectorCalculus[TNBFrame]

VectorCalculus[Torsion]

VectorCalculus[Vector]

 


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