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Student[VectorCalculus]

  

RadiusOfCurvature

  

compute the radius of curvature of a curve

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RadiusOfCurvature(C, t, options)

Parameters

C

-

free or position Vector; specify the components of the curve

t

-

(optional) name; specify the parameter of the curve

options

-

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

Description

• 

The RadiusOfCurvature(C, t) calling sequence computes the radius of curvature of the curve C.  This is defined to be 1/Curvature(C, t) when the curvature is not zero and infinity when the curvature is zero.

• 

If t is not specified, the command tries to determine a suitable variable name from 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, this 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.

  

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

  

* output = plot returns a plot of the space curve and the circles. The number of circles is specified by the circles option. The RadiusOfCurvature command supports only three-dimensional Vector plots.

  

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

• 

circleoptions = list

  

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

• 

circles = posint

  

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

• 

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 [].

• 

range = realcons..realcons

  

The range of the independent variable. The default value is 0..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]:

RadiusOfCurvaturePositionVectorcost,sint,t

2

(1)

RadiusOfCurvaturecost,sint,t

2

(2)

simplifyCurvaturecost,sint,t

12

(3)

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

RadiusOfCurvaturecost,sint,t,output=animation,scaling=constrained

RadiusOfCurvaturecost,sint,t,output=animation,circles=20,scaling=constrained,range=0..10

The command to create the plot from the Plotting Guide is

RadiusOfCurvaturecost,sint,t,output=plot,circles=3,range=0..10,scaling=constrained,curveoptions=orientation=60,270

See Also

realcons

Student[VectorCalculus]

Student[VectorCalculus][Binormal]

Student[VectorCalculus][Curvature]

Student[VectorCalculus][GetCoordinates]

Student[VectorCalculus][PrincipalNormal]

Student[VectorCalculus][SetCoordinates]

Student[VectorCalculus][SpaceCurve]

Student[VectorCalculus][SpaceCurveTutor]

Student[VectorCalculus][TangentVector]

Student[VectorCalculus][TNBFrame]

Student[VectorCalculus][Torsion]

Student[VectorCalculus][Vector]

VectorCalculus

VectorCalculus[RadiusOfCurvature]

 


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