Dr. Sarah's Maple File for Homework 2Plot, Velocity, Acceleration, Jerk, Speed, ArcLength, Curvature, and TorsionModify the coordinate functions of the parameterization. Be sure to keep them as functions of t (and don't forget to hit return): x:=2*cos(3*t);y:=4*sin(t);z:=5*t;If you desire a different domain for the parameterization then modify the 0 and 2*Pi:t_1:=0;t_2:=2*Pi;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.with(VectorCalculus):with(plots):
spacecurve([x,y,z],t=t_1..t_2,axes=frame);
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[1]^2+velocity[2]^2+velocity[3]^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 AnimationModify 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=0..3*Pi command.
You can also change the speed via the number of frames.with(Student[VectorCalculus]):
TNBFrame(<2*sin(t)-sin(2*t),2*cos(t)-cos(2*t),0>,range=0..3*Pi,output=animation,scaling=constrained,axes=frame,frames=50);