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Quart of Ellipse - Ellipse of Inertia

Quart of Ellipse - Ellipse of Inertia
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2014-02-28 19:56
VectorParametric Equation
This example demonstrates a quarter of an ellipse and its ellipse of inertia. Key mathematical concepts include ellipses, moments, and parametric equations. Using GeoGebra commands such as Point, Vector, Rotate, and Segment, the construction of the ellipse of inertia is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point({x_t, y_t}) → t
  2. Vector(t, BodX) → osax
  3. Vector(t, BodY) → osay
  4. Vector(t, BodXc) → osaxc
  5. Vector(t, BodYc) → osayc
  6. Rotate(ElipsaPOM, α, t) → ElipsaSetrvacnosti
  7. Segment(O, BA) → segA
  8. Segment(BB, O) → segB
  9. If((a > 0) ∧ (b > 0), 0, If[(a < 0) ∧ (b > 0), 1.5707963267948966, If[(a < 0) ∧ (b < 0), 3.141592653589793, 4.71238898038469]]) → t1
  10. If((a > 0) ∧ (b > 0), 1.5707963267948966, If[(a < 0) ∧ (b > 0), 3.141592653589793, If[(a < 0) ∧ (b < 0), 4.71239, 0]]) → t2
  11. If(abs(a) < abs(b), t1 - π / 2, t1) → t12
  12. If(abs(a) < abs(b), t2 - π / 2, t2) → t22
  13. Sector(f, t12, t22) → ctvrtelipsa

AI Drawing Prompt Reference

Draw a quarter of an ellipse and its ellipse of inertia. Start by plotting the ellipse, then draw vectors from a point on the ellipse towards the major and minor axes, and also draw vectors towards the major and minor axes of the ellipse of inertia. Connect the origin to a point on the ellipse and draw line segments from the point on the ellipse to the origin. Based on the parameters of the ellipse, calculate and draw a sector representing a quarter of the ellipse.
The prompt above was compiled from the original drawing commands and is for reference only.