compute a Vector in the direction of the binormal vector to a curve in R^3 - Maple Help

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VectorCalculus[Binormal] - compute a Vector in the direction of the binormal vector to a curve in R^3

Calling Sequence

Binormal(C, t, n)

Parameters

C

-

free or position Vector or Vector valued procedure; specify the components of the curve in R^3

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 Binormal(C, t) command computes a Vector in the direction of the binormal vector  to a curve in R^3.  Note that this Vector is not normalized by default, so it is a scalar multiple of the unit binormal vector to the curve C. Therefore, by default, the result is generally different from the output of TNBFrameC,t,output='B'.

• 

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 can be specified as a free or position Vector or a Vector valued procedure. This determines the returned object type. However, it must have exactly three components, that is, the curve that the Vector or Vector valued procedure represents is in R^3.

• 

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 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:

Binormalcost,sint,t,t

12sint12cost12

(1)

Binormalⅇtcost,ⅇtsint,t

2ⅇtcost2ⅇ2t+12ⅇtsint2ⅇ2t+12ⅇ2t2ⅇ2t+1

(2)

B1:=Binormalt→t,t2,t3:

B1t

6t29t4+4t2+16t9t4+4t2+129t4+4t2+1

(3)

B2:=Binormalt→t,t2,t3,normalized:

B2t

3t29t4+9t2+19t4+4t2+129t4+4t2+13t9t4+9t2+19t4+4t2+129t4+4t2+119t4+9t2+19t4+4t2+129t4+4t2+1

(4)

SetCoordinates'cylindrical'

cylindrical

(5)

Binormala,t,tassuminga::Andpositive,constant

0aa2+1a2a2+1

(6)

See Also

VectorCalculus, VectorCalculus[Curvature], VectorCalculus[GetCoordinates], VectorCalculus[PrincipalNormal], VectorCalculus[RadiusOfCurvature], VectorCalculus[SetCoordinates], VectorCalculus[TangentVector], VectorCalculus[TNBFrame], VectorCalculus[Torsion], VectorCalculus[Vector]


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