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MA 242.003

MA 242.003 . Day 15- January 28, 2013 Chapter 10, section 10.4. Goal : Use calculus to describe the geometry of curves in 3-space. Goal : Use calculus to describe the geometry of curves in 3-space. Goal : Use calculus to describe the geometry of curves in 3-space.

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MA 242.003

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  1. MA 242.003 • Day 15- January 28, 2013 • Chapter 10, section 10.4

  2. Goal: Use calculus to describe the geometry of curves in 3-space

  3. Goal: Use calculus to describe the geometry of curves in 3-space

  4. Goal: Use calculus to describe the geometry of curves in 3-space

  5. Goal: Use calculus to describe the geometry of curves in 3-space

  6. Goal: Use calculus to describe the geometry of curves in 3-space

  7. We have a good definition of curvature.

  8. We have a good definition of curvature. P

  9. We have a good definition of curvature. P Q

  10. A few more osculating circles:

  11. Section 10.4

  12. Section 10.4

  13. Section 10.4

  14. Section 10.4

  15. Section 10.4 We now have the tools to describe the acceleration vector

  16. (continuation of proof)

  17. Tangential component of acceleration

  18. Tangential component of acceleration Normal component of acceleration

  19. Tangential component of acceleration Normal component of acceleration We reformulate the formula for NORMAL COMPONENT

  20. Tangential component of acceleration Normal component of acceleration New formulas for and .

  21. (continuation of calculation)

  22. Tangential component of acceleration Normal component of acceleration New formulas for and .

  23. Tangential component of acceleration Normal component of acceleration New formulas for and .

  24. Tangential component of acceleration Normal component of acceleration New formulas for and .

  25. (continuation of example)

  26. Example: Motion in a circle at constant speed:

  27. Example: Motion in a circle at constant speed: Centripetal Acceleration

  28. (continuation of calculation)

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