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Student[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 Vector-valued procedure; specify the components of the curve

t

-

(optional) name; specify the parameter of the curve

Description

• 

The Curvature(C, t) calling sequence 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 that 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 curve and the coordinate system are incompatible, an error is returned.

Examples

withStudent[VectorCalculus]:

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)

SetCoordinatespolar

polarr,θ

(5)

Curvatureⅇt,t

12122ⅇtcostⅇtsintⅇ2t+2ⅇtsintⅇ2t2+122ⅇtsint+ⅇtcostⅇ2t2ⅇtcostⅇ2t22ⅇ2t

(6)

simplifyassumingt::real

122ⅇt

(7)

See Also

assuming

Student[VectorCalculus]

Student[VectorCalculus][Binormal]

Student[VectorCalculus][GetCoordinates]

Student[VectorCalculus][PrincipalNormal]

Student[VectorCalculus][RadiusOfCurvature]

Student[VectorCalculus][SetCoordinates]

Student[VectorCalculus][TangentVector]

Student[VectorCalculus][TNBFrame]

Student[VectorCalculus][Torsion]

Student[VectorCalculus][Vector]

 


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