Dr. Sarah's Maple File for TNB1 Be sure to keep the coordinate functions of the parameterization as functions of t (and don't forget to hit return): with(Student[VectorCalculus]): with(plots): x:=r*cos(w*t); y:=r*sin(w*t); z:=0; If you desire a different domain for the parameterization then modify the t_1 and t_2 to have different values: t_1:=0; t_2:=2*Pi/3; Velocity, Acceleration, Jerk, Speed, ArcLength, Curvature, and Torsion Hit return for this without modification. Depending on the parameterization, it may take a while. If need be, you can stop it from continuing via the symbol that is an octagon with an exclamation point inside of it. velocity:= diff([x,y,z],t); acceleration:= diff(diff([x,y,z],t),t); jerk:= diff(diff(diff([x,y,z],t),t),t); speed := simplify(sqrt(velocity^2+velocity^2+velocity^2)); arclength:= ArcLength(<x,y,z>,t=t_1..t_2); curvature:=simplify(Curvature(<x,y,z>,t),trig); torsion:=simplify(Torsion(<x,y,z>,t),trig); TNB, Plot, and TNB Animation Modify the x, y, and z coordinates of the parametrization in the TNBFrame command below. If you desire then you can modify the domain for the parametrization by changing the range=t_1 and t_2 command. You can also change the speed of the animation via the number of frames and the thickness of the vectors as in the "output=plot" version below. TNBFrame(<x,y,z>,t); curveplot:=spacecurve([x,y,z],t=t_1..t_2,axes=frame); TNBFrame(<x,y,0>,range=t_1..t_2,output=animation,scaling=constrained,axes=frame,frames=50); TNBFrame(<x,y,z>,range=t_1..t_2,output=plot,scaling=constrained, axes=frame,curveoptions=[color="LightBlue", linestyle=dot],tangentoptions=[color=black, width=.01], normaloptions=[width=.01], binormaloptions=[width=.01], frames=7); x:=2*cos(3*t); y:=2*sin(3*t); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv