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Elliptical Trajectories Models

Elliptical Trajectories Models
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2018-07-29 04:05
TrigonometryCoordinate GeometryParametric Equation
This example demonstrates the geometric construction of elliptical trajectories. Key mathematical concepts include the definition of an ellipse, parametric equations, and rotation transformations. By adjusting parameters a, b, θ, etc., the shape of the ellipse can be observed. Suitable for high school and above students to learn about ellipses.

GeoGebra Commands & Parameters

  1. Numeric a(2.5)
  2. Numeric b(5)
  3. (x / a)^(2) + (y / b)^(2) = 1
  4. Angle θ(1.864011641129944)
  5. ((a * cos(θ)), (b * sin(θ)))
  6. Numeric CR(0.42)
  7. Numeric CG(0.58)
  8. Numeric CB(0.92)
  9. ((a * cos(θ)), (b * sin(θ)), sqrt(((a * cos(θ)))^(2) + ((b * sin(θ)))^(2)))
  10. ((a * cos(θ)), (b * sin(θ)), (a * cos(θ)) + (b * sin(θ)))
  11. ((a * cos(θ)), (b * sin(θ)), ((-a) * cos(θ)) - (b * sin(θ)))