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System of Differential Equations in Phase Plane

System of Differential Equations in Phase Plane
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2016-12-07 08:48
VectorCoordinate GeometryCalculusOptimizationParametric Equation
This example demonstrates trajectories and vector fields of a system of differential equations in the phase plane. Key mathematical concepts include differential equations, phase plane analysis, vector fields, and isoclines. Construction highlights the use of GeoGebra commands and objects such as SlopeField (vector field), Textfield (text input), SolveODE (solving ODEs), Vector (vectors), UnitVector (unit vectors), and ImplicitCurve (implicit curves). Suitable for university students in mathematics, physics, or engineering for understanding dynamical systems and stability analysis.

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 of a system of differential equations, including the slope field, vector field, solution curves, unit vectors, and isoclines. First, draw the slope field, then input the expressions for u and v, solve the differential equations to get the solution curves, and finally draw the unit vectors and isoclines.
The prompt above was compiled from the original drawing commands and is for reference only.