Curvature Package
![r[t_] := {t, 2 t^2, t^(-1)}; k[r][t]](images/CurvaturePics_gr_1.gif)
![Plot[%, {t, 0, 2}]](images/CurvaturePics_gr_3.gif)
Synopsis
This package provides commands for calculating the curvature of a parametrically defined curve in the plane or in space. Also included are commands for calculating unit tangent and unit normal vectors, and commands for animating images of the osculating circle and the evolute of the curve.
Commands
The following commands are provided in this package:
\[Kappa][r][t]
gives the curvature of the parametric curve r with paramter t.
Norm[v]
calculates the norm of the vector v.
OsculatingCircleMovie[r,{t,tmin,tmax}]
produces an animation of the
osculating circle of the curve r[t] as it moves about the curve. The option
Frames determines the number of frames in the movie. Note that PlotRange
should generally be used to set a sensible plot range.
EvoluteMovie[r,{t,tmin,tmax}]
produces an animation of the osculating
circle of the curve r[t] as it moves about the curve and traces the Evolute
of the curve. The option Frames determines the number of frames in the movie.
Note that PlotRange should generally be used to set a sensible plot range.
UnitNormal[r][t]
gives the unit normal vector to the parameterized curve r with parameter t.
UnitTangent[r][t]
gives the unit tangent vector to the parameterized curve r
with parameter t.
Last Updated: February 26, 2004