Dr. Sarah's Maple File for TNB2 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): Lemniscate of Myka x:=(t+t^3)/(1+t^4); y:=(t-t^3)/(1+t^4); 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:=-10; t_2:=10; Lemniscate of Myka 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); Lemniscate of Myka TNB, Plot, TNB Animation, and Osculating Circle 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); TNBFrame(<(t+t^3)/(1+t^4), (t-t^3)/(1+t^4),0>) assuming t::real ; TNBFrame(<(t+t^3)/(1+t^4), (t-t^3)/(1+t^4),0>) assuming t::real, 0<t ; curveplot:=spacecurve([x,y,z],t=t_1..t_2,axes=frame); TNBFrame(<x, y,z>,range=t_1..t_2,output=animation,scaling=constrained, axes=frame,frames=50,curveoptions=[color="Blue", linestyle=dot],tangentoptions=[color=black, width=.02], normaloptions=[width=.02], binormaloptions=[width=.02]); 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=6); RadiusOfCurvature(<x,y,z>,t,range=.1..10, output=animation,scaling=constrained, circles=50); RadiusOfCurvature(<x,y,z>,range=.1..10,output=plot,scaling=constrained, axes=frame,curveoptions=[color="LightBlue", linestyle=dot]); Mystery Curve x:=5/13*cos(t); y:=-sin(t) z:=-12/13*cos(t); 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; Mystery Curve 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); Mystery Curve 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,z>,range=t_1..t_2,output=animation,scaling=constrained, axes=frame,frames=20,curveoptions=[color="Blue", linestyle=dot],tangentoptions=[color=black, width=.02], normaloptions=[width=.02], binormaloptions=[width=.02]); 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=6);