MathPlotAI Logo MathPlotAI

Parametric Motion Lab

Parametric Motion Lab
Loading the math board and drawing, please wait…
2016-06-11 00:45
VectorCalculusDerivativeParametric EquationSlider Animation
① This example demonstrates a point moving along a parametric curve, showing its trajectory, velocity and acceleration vectors in real time. ② Core mathematical concepts: parametric equations, first and second derivatives, vector decomposition, real‑valued functions, and an intuitive link to confidence intervals. ③ Construction highlights: CurveCartesian draws the parametric curve; Vector creates velocity/acceleration vectors; Derivative computes dfdt, dgdt, d2fdt, d2gdt; Textfield and InputBox1/2 provide interactive parameter control; key objects include g, f, t, a_1, u, vel, v, vx, vy, a, A, B, w, b, C, start, c. ④ Suitable for high‑school calculus electives, introductory university calculus lectures, and teacher preparation materials.

GeoGebra Commands & Parameters

  1. CurveCartesian(f(t), g(t), t, 0, 49) → a_1
  2. Vector((0, 0), a_1(t)) → u
  3. Derivative(f) → dfdt
  4. Derivative(g) → dgdt
  5. Vector((dfdt(t), dgdt(t))) → vel
  6. Vector((f(t), g(t)), (f(t) + dfdt(t), g(t) + dgdt(t))) → v
  7. Vector((f(t), g(t)), (f(t) + dfdt(t), g(t))) → vx
  8. Vector((f(t), g(t)), (f(t), g(t) + dgdt(t))) → vy
  9. Derivative(dfdt) → d2fdt
  10. Derivative(dgdt) → d2gdt
  11. Vector((f(t), g(t)), (f(t) + d2fdt(t), g(t) + d2gdt(t))) → a
  12. Vector((0, g(t)), (0, g(t) + dgdt(t))) → w
  13. Vector((f(t), 0), (f(t) + dfdt(t), 0)) → b
  14. CurveCartesian(dfdt(t), dgdt(t), t, 0, 49) → c
  15. Textfield(f) → InputBox1
  16. Textfield(g) → InputBox2

AI Drawing Prompt Reference

Draw a planar curve defined by parametric functions f(t) and g(t), place a point that moves along the curve as t varies, and show the velocity vector at that point together with its horizontal and vertical components; also display the acceleration vector. In a separate coordinate system plot the hodograph – the trajectory of the velocity vector’s tip. Provide two input fields so the user can change the formulas for f(t) and g(t) interactively.
The prompt above was compiled from the original drawing commands and is for reference only.