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Phase Plane by Pablo Rodríguez-Sánchez

Phase Plane by Pablo Rodríguez-Sánchez
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2016-07-21 21:59
VectorCalculus
This example demonstrates the concept of a phase plane, involving solutions to differential equations. Using GeoGebra commands like SlopeField and Vector, phase trajectories can be visually displayed. Suitable for calculus and ordinary differential equations courses.

GeoGebra Commands & Parameters

  1. SlopeField(v(x, y) / u(x, y), N, l, xmin, ymin, xmax, ymax) → slopefield1
  2. Textfield(u) → InputBox1
  3. Textfield(v) → InputBox2
  4. SolveODE(v(x, y) / u(x, y), x(A), y(A), tmin, numStep) → fAback
  5. SolveODE(v(x, y) / u(x, y), x(A), y(A), tmax, numStep) → fAforw
  6. SolveODE(v(x, y) / u(x, y), x(B), y(B), tmin, numStep) → fBback
  7. SolveODE(v(x, y) / u(x, y), x(B), y(B), tmax, numStep) → fBforw
  8. Vector((u(x(B), y(B)), v(x(B), y(B)))) → VB
  9. UnitVector(VA) → vA
  10. UnitVector(VB) → vB
  11. Vector(A, A + vA) → v_A
  12. Vector(B, B + vB) → v_B
  13. ImplicitCurve(u(x, y)) → IsoclineX
  14. ImplicitCurve(v(x, y)) → IsoclineY
  15. Textfield(numStep) → InputBox3
  16. Textfield(tmax) → InputBox4

AI Drawing Prompt Reference

Draw a phase plane for differential equations, including a direction field and trajectories. Start by plotting the direction field represented by the ratio of two functions, then trace forward and backward from initial points to show trajectories, add unit vectors extending from these points, and finally include isoclines to illustrate slope relationships.
The prompt above was compiled from the original drawing commands and is for reference only.