Dynamics · modes of motion

3D flight-mode simulator

A live 6-DoF linear flight sandbox. Pick an aircraft and the demo builds a coupled small-perturbation model from its real stability and control derivatives, integratingẊ = A·(X + gust) + B·u(t) in real time. Hand-fly it with the on-screen stick and rudder pedals, inject controls or gusts on any axis, and plot whatever signals you like on the time-history chart. The classic modes of motion are built-in presets. Full notes below the demo.

What you're looking at

The grey N / E / D arrows are the Earth (north-east-down) reference; the coloured x_b / y_b / z_b arrows are the aircraft body axes. Use the playbar to pause/resume the live simulation, change the speed, or reset the state and inputs to trim; orbit and zoom with the mouse.
The system matrix A is block-diagonal: the longitudinal[u, w, q, θ] model and (where the airframe has lateral-directional data) the [β, p, r, φ] model. The control matrix B holds the elevator/aileron/rudder columns built from the airframe's control derivatives, and gusts enter by shifting the aero state (vertical gust → w, side gust → β).
The view is earth-fixed (wind axes): the aircraft flies its integrated trajectory with a fading CG trail, and the whole displayed state — attitude andground speed — is scaled by one exaggeration gain so the motion stays faithful (a phugoid speeds up as it sinks and slows as it climbs). Turn on Compare to fly a linear ghost against the full nonlinear model and watch the two trajectories diverge.
The info panel reports the selected mode's natural frequency ω_n and damping ratio ζ (or time constant τ for the non-oscillatory roll and spiral modes) and its period — the same numbers the eigenvalues of the system matrix give.
The inceptors feed their deflections into the same u(t) the inject panel uses, so flying the stick and scripting a doublet are one mechanism; thestrip chart samples the live state every frame, so its traces are exactly what the aircraft is doing in the 3D view.