8. Properties of Curves - Contents

1. Vector Functions, Position, Velocity and Plots

     1   2
   1. Vector Functions: Position and Plots
   2. Vector Functions: Velocity and Force

2. Limits and Derivatives of Vector Functions

     1   2
   1. Limits of Vector Functions
   2. Derivatives of Vector Functions

3. Velocity, Acceleration, and Jerk

     1
   1. Velocity, Acceleration, and Jerk

4. Arc Length, Arc Length Parameter, and Speed

     1   2   3
   1. Arc Length of a Curve
   2. Arc Length Parameter
   3. Speed

5. Tangent, Normal, and Binormal Vectors

     1   2
   1. Definitions
   2. Computational Formulas

6. Curvature and Torsion

     1   2
   1. Curvature
   2. Torsion
      1. Torsion Formula Proof

7. Tangential and Normal Acceleration

     1
   1. Tangential and Normal Acceleration

8. Summary & Examples of Curve Computations

     1   2
   1. Summary of Curve Computations
   2. Examples of Curve Computations
      1. Circle
      2. Helix
      3. Cubic
      4. Cubic Spiral Helix

9. Frenet Frames (Optional)

     1
   1. Frenet Frames & Derivatives of TNB (Optional)

10. Tutorial on Properties of Curves

      1
    1. Tutorial on Properties of Curves

11. Exercises

      1
    1. Exercises