MathPlotAI Logo MathPlotAI

Rational Gravitational Field Model

Rational Gravitational Field Model
Loading the math board and drawing, please wait…
2018-07-29 02:04
VectorFunctionCoordinate GeometryOptimization
This example demonstrates the graphical representation of a rational gravitational field model in a 2D space. It involves core mathematical concepts such as 2D vectors, parabolas, logarithmic functions, area calculation, and centroid. The construction utilizes GeoGebra commands/objects like points CO, CB, CG, CR, parameters a, n, text objects texto1, texto2, coordinate points x_o, y_o, function object fm, slider α, and area A. It is suitable for high school and above students to learn and understand the application of physical and mathematical concepts like gravitational fields and centroids in analytical geometry.

GeoGebra Commands & Parameters

  1. Numeric CO(0.37)
  2. Numeric CB(0)
  3. Numeric CG(0)
  4. Numeric CR(0)
  5. Numeric a(1.15)
  6. Numeric n(2)
  7. Numeric x_o(0)
  8. Numeric y_o(0)
  9. fm(x, y) = ((-a)) / ((x - x_o)^(2) + (y - y_o)^(2))^(n)
  10. Numeric r(2.46)
  11. Angle α(3.18871654339364)
  12. (x_o + (r * cos(α)), y_o + (r * sin(α)), fm(x_o + (r * cos(α)), y_o + (r * sin(α))))