2. Homework Aid: Cycloid Motion
Chapter 13
13.2 Modeling Projectile Motion
Homework Aid: Cycloid Motion

3. The Vector and Parametric Equations for Ideal Projectile Motion
Chapter 13
13.2 Modeling Projectile Motion
The Vector and Parametric Equations for Ideal Projectile Motion

4. The Vector and Parametric Equations for Ideal Projectile Motion
Chapter 13
13.2 Modeling Projectile Motion
The Vector and Parametric Equations for Ideal Projectile Motion
Example

5. Arc Length Along a Space Curve
Chapter 13
13.3 Arc Length and the Unit Tangent Vector T
Arc Length Along a Space Curve

6. Arc Length Along a Space Curve
Chapter 13
13.3 Arc Length and the Unit Tangent Vector T
Arc Length Along a Space Curve
Example

7. Arc Length Along a Space Curve
Chapter 13
13.3 Arc Length and the Unit Tangent Vector T
Arc Length Along a Space Curve

8. Speed on a Smooth Curve, Unit Tangent Vector T
Chapter 13
13.3 Arc Length and the Unit Tangent Vector T
Speed on a Smooth Curve, Unit Tangent Vector T

9. Speed on a Smooth Curve, Unit Tangent Vector T
Chapter 13
13.3 Arc Length and the Unit Tangent Vector T
Speed on a Smooth Curve, Unit Tangent Vector T
Example

10. Curvature of a Plane Curve
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature of a Plane Curve

11. Curvature of a Plane Curve
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature of a Plane Curve
Example

12. Curvature of a Plane Curve
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature of a Plane Curve

13. Curvature of a Plane Curve
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature of a Plane Curve
Example

14. Curvature and Normal Vectors for Space Curves
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature and Normal Vectors for Space Curves

15. Curvature and Normal Vectors for Space Curves
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature and Normal Vectors for Space Curves
Example
Effects of increasing a or b?
Effects on reducing a or b to zero?

16. Curvature and Normal Vectors for Space Curves
Chapter 13
13.4 Curvature and the Unit Normal Vector N
Curvature and Normal Vectors for Space Curves
Example

17. Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Torsion
As we are traveling along a space curve, the Cartesian i, j, and k coordinate system which are used to represent the vectors of the motion are not truly relevant.
Instead, it is more meaningful to know the vectors representative of our forward direction (unit tangent vector T), the direction in which our path is turning (the unit normal vector N), and the tendency of our motion to twist out of the plane created by these vectors in a perpendicular direction of the plane (defined as unit binormal vector B = T  N).

18. Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Torsion

19. Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Torsion

20. Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Torsion

21. Tangential and Normal Components of Acceleration
Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Tangential and Normal Components of Acceleration

22. Tangential and Normal Components of Acceleration
Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Tangential and Normal Components of Acceleration

23. Tangential and Normal Components of Acceleration
Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Tangential and Normal Components of Acceleration
Example

24. Tangential and Normal Components of Acceleration
Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Tangential and Normal Components of Acceleration

25. Homework 3 Exercise 13.2, No. 7. Exercise 13.3, No. 5.
Chapter 13
13.5 Torsion and the Unit Binormal Vector B
Homework 3
Exercise 13.2, No. 7.
Exercise 13.3, No. 5.
Exercise 13.3, No. 12.
Exercise 13.4, No. 3.
Exercise 13.4, No. 11.
Exercise 13.5, No. 12.
Exercise 13.5, No. 24.
Due: Next week, at