Arc Length and Curvature: Examples

1. FInd the arc length of the following function from t=0 to t=3: <t^2,3/2*t^2,t>

Anwser:
Use the ArcLength command. Note: we need to activate the VectorCalculus package

>	with(VectorCalculus);

>	ArcLength(<t^2,3/2*t^2,t>,t=0..3);

We can also graph the curve using the space curve function:

>	spacecurve([t^2,3/2*t^2,t],t=0..3);

2. Find the Tangent, Normal, and Binormal vectors of the following vector: <2*cos(t),2*sin(t),t/2>

Anwser:
To find these vectors in Maple is ALOT easier than it would be to do it by hand, we can simply use the command TBNFrame to find all the vectors.

>	TNBFrame(<2*cos(t),2*sin(t),t/2>,t);

3. Find the curvature of the following equation: <t,t^2,t^2/2>

>	Curvature(<t,t^2,t^2/2>,t);

>	simplify(%);