For K-12 Students · State-Space Phase Portrait
State-Space Phase Portrait for a quadruped
Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a quadruped live below — adjust the inputs and watch it respond, right in your browser.
State-Space Phase PortraitLive
the shape of a linear system
Controls
Presets
A linear state-space system ẋ = Ax has a character set by the eigenvalues of A. Negative real parts spiral or decay to the origin (stable); positive parts fly outward; imaginary parts add rotation. The phase portrait reveals it all at a glance. Educational tool.
Data Inspector
Trace / Det-0.30 / 1.00
Eigenvalues-0.15 ± 0.99j
Classificationstable spiral
Governing equation
Reading this result: Complex eigenvalues with negative real part: trajectories spiral inward, oscillating while decaying to the origin — a stable, ringing system.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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Frequently asked questions
- Is this good for k-12 students?
- Yes — this version of "State-Space Phase Portrait for a quadruped" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.