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Student[VectorCalculus]

  

TNBFrame

  

compute the tangent-normal-binormal frame of a curve in R^3

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

TNBFrame(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, binormal, binormaloptions, curveoptions, frames, normal, normaloptions, range, tangent, tangentoptions, or view

Description

• 

The TNBFrame(C, t, out) calling sequence computes the tangent-normal-binormal frame of the curve C, that is, the unit tangent, normal, and binormal Vectors.  The computed objects are returned in an expression sequence.

• 

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, the single 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. The output is always returned in the order: tangent, normal, binormal.

  

* 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 TNB frames. The number of TNB frames is specified by the frames option.

  

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

• 

binormal = truefalse

  

Controls whether the binormal vector is included in the output or plot. The default value is true.

• 

binormaloptions = list

  

A list of plot options for plotting the binormal portion of the TNB frame. For more information on plotting options, see plot/options. The default value is []. Note: Vectors are plotted using plots[arrow].

• 

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 [].

• 

frames = posint

  

Specifies how many TNB frames are to be plotted or animated. The default value is 5.

• 

normal = truefalse

  

Controls whether the normal vector is included in the output or plot. The default value is true.

• 

normaloptions = list

  

A list of plot options for plotting the normal portion of the TNB frame. For more information on plotting options, see plot/options. The default value is []. Note: Vectors are plotted using plots[arrow].

• 

range = realcons..realcons

  

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

• 

tangent = truefalse

  

Controls whether the tangent vector is included in the output or plot. The default value is true.

• 

tangentoptions = list

  

A list of plot options for plotting the tangent portion of the TNB frame. For more information on plotting options, see plot/options. The default value is []. Note: Vectors are plotted using plots[arrow].

• 

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]:

TNBFramecost,sint,t,t

122sint122cost122,costsint0,122sint122cost122

(1)

TNBFramePositionVectorcost,sint

sintcost,costsint

(2)

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.

TNBFramecost,sint,t3,range=0..2π,output=animation,scaling=constrained,axes=frame,frames=15

SetCoordinatescylindricalr,t,z

cylindricalr,t,z

(3)

TNBFrame1,t,t

12costcossint2sint+12cost2sinsint2cost2sinsint2+cost2cossint212cost2cossint2+12costsinsint2sintcost2sinsint2+cost2cossint2122,cost2cossintcostsinsintsintcost2sinsint2+cost2cossint2costcossintsint+cost2sinsintcost2sinsint2+cost2cossint20,12costcossint2sint12cost2sinsint2cost2sinsint2+cost2cossint212cost2cossint212costsinsint2sintcost2sinsint2+cost2cossint2122

(4)

SetCoordinatescartesian

cartesian

(5)

The command to create the plot from the Plotting Guide is

TNBFramecost,sint,t,output=plot,binormal=false,scaling=constrained,normaloptions=orientation=240,130

See Also

realcons

Student[VectorCalculus]

Student[VectorCalculus][Binormal]

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][Torsion]

VectorCalculus

VectorCalculus[TNBFrame]

 


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