Curve Visualization
Parameters
Appearance
About Lissajous Curves
Lissajous curves, also known as Lissajous figures or Bowditch curves, are the graphs of a system of parametric equations that describe complex harmonic motion.
Mathematical Formula
x = A × sin(a × t + δ)
y = B × sin(b × t)
y = B × sin(b × t)
Where:
- A, B: Amplitudes of the waves
- a, b: Frequencies of the waves
- δ: Phase difference between the waves
- t: Time parameter
Common Examples
Circle
a=1, b=1, δ=0
Ellipse
a=1, b=1, δ=π/2
Classic Curve
a=3, b=2, δ=π/2
Complex Pattern
a=5, b=4, δ=π/2
Applications
Lissajous curves have applications in physics, astronomy, and engineering:
- Oscilloscopes for signal analysis
- Harmonic oscillators in mechanics
- Optics and wave interference
- Art and design patterns