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

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

Calling Sequence

Binormal(C, t, options)

Parameters

C

-

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

t

-

(optional) name; specify the parameter of the curve

options

-

(optional) equation(s) of the form option=value where option is one of output, curveoptions, normalized, range, vectoroptions, vectors, or view

Description

• 

The Binormal(C, t) calling sequence computes a Vector in the direction of the binormal vector  to a curve in R^3.

  

Note: 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 TNBFrame(C, t, binormal=true). If either normalized=true or normalized is given in options, however, the resulting vector will be normalized.

• 

The curve C must have exactly three components, that is, the curve that the Vector represents is in R^3.

• 

If t is not specified, the command 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 entry is the variable name.  If it has more than one entry, an error is raised.

• 

The options arguments primarily control plot options.

  

output = value, plot, or animation

  

This option controls the return value of the command.

  

* output = value returns the value of the binormal. Plot options are ignored if output = value. This is the default value.

  

* output = plot returns a plot of the space curve and the binormal vectors. The number of binormal vectors is specified by the vectors option.

  

* output = animation returns an animation of the space curve and the binormal vectors. The number of binormal vectors is specified by the vectors option.

• 

curveoptions = list

  

A list of plot options for plotting the space curve. For more information on plotting options, see plot/options. The default value is [].

• 

normalized = truefalse

  

Either true or false. Specifies whether the binormal vector is to be normalized. The default value is false.

• 

range = realcons..realcons

  

The range of the independent variable. The default value is 0..5.

• 

vectoroptions = list

  

A list of plot options for plotting the binormal vectors. For more information on plotting options, see plot/options. The default value is [].

• 

vectors = posint

  

Specifies how many binormal vectors are to be plotted or animated. The default value is 5.

• 

view = [realcons..realcons, realcons..realcons, realcons..realcons]

  

Specify the plot view. For more information see plot3d/options.

• 

caption = anything

  

A caption for the plot.

  

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.

Examples

withStudent[VectorCalculus]:

BinormalPositionVectorcost,sint,t,t

12sint12cost12

(1)

BinormalPositionVectorcost,sint,t,t,normalized

122sint122cost122

(2)

Binormalⅇtcost,ⅇtsint,t

2ⅇtcost2ⅇ2t+12ⅇtsint2ⅇ2t+12ⅇ2t2ⅇ2t+1

(3)

Binormalcost,sint,t,t,output=plot,scaling=constrained

Binormalcost,sint,t,output=plot,scaling=constrained

Binormalcost,sint,t,t,output=plot,range=0..7,vectors=15,vectoroptions=color=red,curveoptions=color=green,scaling=constrained

To play the following animation in this help page, right-click (Control-click, on Macintosh) the plot to display the context menu.  Select Animation > Play.

Binormalcost,sint,t,t,output=animation,range=0..7,vectors=50,vectoroptions=color=red,curveoptions=color=green,scaling=constrained

SetCoordinatescylindricalr,t,z

cylindricalr,t,z

(4)

Binormala,t,tassuminga::Andpositive,constant

0aa2+1a2a2+1

(5)

See Also

assuming, plot3d/options, realcons, Student[VectorCalculus], Student[VectorCalculus][Curvature], Student[VectorCalculus][GetCoordinates], Student[VectorCalculus][PrincipalNormal], Student[VectorCalculus][RadiusOfCurvature], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][SpaceCurve], Student[VectorCalculus][SpaceCurveTutor], Student[VectorCalculus][TangentVector], Student[VectorCalculus][TNBFrame], Student[VectorCalculus][Torsion], Student[VectorCalculus][Vector], VectorCalculus, VectorCalculus[Binormal]


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