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VectorCalculus

  

PrincipalNormal

  

compute a Vector in the direction of the principal normal vector to a curve

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PrincipalNormal(C, t, n)

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

n

-

(optional) equation of the form normalized=true or normalized=false, or simply normalized

Description

• 

The PrincipalNormal(C, t) command computes a Vector in the direction of the principal normal vector to the curve C.  Note that this vector is not normalized by default, so it is a scalar multiple of the unit normal vector to the curve C. Therefore, by default, if C is a curve in R^3, the result is generally different from the output of TNBFrame(C, t, output=['N']).

• 

If n is given as either normalized=true or normalized, then the resulting vector will be normalized before it is returned. As discussed above, the default value is false, so that the result is not normalized.

• 

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, C is interpreted in that 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:

PrincipalNormalcost,sint,t

costsint

(1)

PrincipalNormalPositionVectorcost,sint,t

122cost122sint0

(2)

P1PrincipalNormalt→t,t2,t3:

P1t

2t9t2+29t4+4t2+13/229t419t4+4t2+13/26t2t2+19t4+4t2+13/2

(3)

P2PrincipalNormalt→t,t2,t3,normalized:

P2t

t9t2+29t4+9t2+19t4+4t2+129t4+4t2+13/29t419t4+9t2+19t4+4t2+129t4+4t2+13/23t2t2+19t4+9t2+19t4+4t2+129t4+4t2+13/2

(4)

SetCoordinates'polar'

polar

(5)

PrincipalNormala&ExponentialE;t&comma;tassuminga::constant&comma;0<a

122122

(6)

See Also

VectorCalculus

VectorCalculus[Binormal]

VectorCalculus[Curvature]

VectorCalculus[GetCoordinates]

VectorCalculus[RadiusOfCurvature]

VectorCalculus[SetCoordinates]

VectorCalculus[TangentVector]

VectorCalculus[TNBFrame]

VectorCalculus[Torsion]

VectorCalculus[Vector]