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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\:$

$\mathrm{RadiusOfCurvature}\left(\mathrm{PositionVector}\left(\left[\cos \left(t\right)\,\sin \left(t\right)\,t\right]\right)\right)$

$2$

$\mathrm{RadiusOfCurvature}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\right)$

$2$

$\mathrm{simplify}\left(\mathrm{Curvature}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\right)\right)$

$\frac{1}{2}$

$\mathrm{RadiusOfCurvature}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\,\mathrm{output}=\mathrm{animation}\,\mathrm{scaling}=\mathrm{constrained}\right)$

$\mathrm{RadiusOfCurvature}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\,\mathrm{output}=\mathrm{animation}\,\mathrm{circles}=20\,\mathrm{scaling}=\mathrm{constrained}\,\mathrm{range}=0..10\right)$

$\mathrm{RadiusOfCurvature}\left(⟨\cos \left(t\right)\,\sin \left(t\right)\,t⟩\,\mathrm{output}=\mathrm{plot}\,\mathrm{circles}=3\,\mathrm{range}=0..10\,\mathrm{scaling}=\mathrm{constrained}\,\mathrm{curveoptions}=\left[\mathrm{orientation}=\left[60\,270\right]\right]\right)$