Homework Aid: Cycloid Motion

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

25. 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 17.15.