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Parametric Equations

Parametric Equations. HW: 11.1; 3,22. Why do we need parametric equations?. Consider the flight of a golf ball…the motion consists of two independent parts (Galileo’s “big” insight): Falling motion or Galileo’s Law of falling bodies in the vertical (y) direction

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Parametric Equations

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  1. Parametric Equations HW: 11.1; 3,22

  2. Why do we need parametric equations? • Consider the flight of a golf ball…the motion consists of two independent parts (Galileo’s “big” insight): • Falling motion or Galileo’s Law of falling bodies in the vertical (y) direction • Uniform translational motion in the horizontal (x) direction

  3. “In Math”… • Vertical motion: • Horizontal motion: “t” is the parameter

  4. What path does a golf ball follow? But how are x and y related to each other?

  5. A famous historical example … the Cycloid • What path does a point on the rim of a circle trace as the circle rolls at a constant rate without slipping?

  6. So, why do we need parametric equations? • By finding the suitable parameterization you can sometimes express relationships between variables that would otherwise be very difficult to do.

  7. Next lecture… • Applying ideas of calculus to parametric equations • Read 11.2 • HW: 3, 15

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