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Phase Plane

Phase Plane
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2020-01-12 02:05
VectorCalculusDerivative
This example demonstrates the phase plane of differential equations, visualizing system dynamics through vector fields and trajectories. Core math concepts include differential equations, vector fields, trajectories, and isoclines. Construction highlights the use of GeoGebra commands/objects like SlopeField, Textfield, SolveODE, Vector, UnitVector, and ImplicitCurve. Suitable for university students in mathematics, physics, and related fields studying dynamic systems.

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