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Advanced State Space Phase Portrait
dx/dt = Ax | Interactive Dynamics, Animation, & Time Response
System Matrix (A)
A =
Presets
Damped Oscillator (Stable Focus)
Harmonic Oscillator (Center)
Saddle Point
Overdamped (Stable Node)
Unstable Node
Unstable Focus
Vector Field Density
Medium (40px)
Update Vector Field
Clear Trajectories
Left Click:
Drop Particle |
Right-Click Drag:
Pan |
Scroll:
Zoom
System Response x(t) (Last Clicked Trajectory)
Key Concepts
State Equations
ẋ = Ax + Bu, y = Cx + Du
Stability via Eigenvalues
System is stable if and only if all eigenvalues of A have negative real parts.
Controllability
Check rank(C) = n, where C = [B AB A²B…]. Full rank → fully controllable.