Longitudinal Flight Dynamics Lab

SIMULATION ▼

SHORT PERIOD MODE ▼

FREQUENCY (ω_sp) 3.00rad/s

DAMPING (ζ_sp) 0.60

PHUGOID MODE ▼

FREQUENCY (ω_ph) 0.15rad/s

DAMPING (ζ_ph) 0.05

INITIAL CONDITIONS ▼

VELOCITY DEV. (u) 0.0m/s

V. VELOCITY DEV. (w) 0.0m/s

PITCH RATE (q) 0.0deg/s

PITCH ANGLE (θ) 0.0deg

CONTROL INPUTS ▼

INPUT TYPE

ELEVATOR AMPLITUDE (δ_e) 0.0deg

THROTTLE AMPLITUDE (δ_t) 0.00

EIGENMODE INITIALIZER ▼

SELECT EIGENVALUE FOR MODAL INIT

3D FLIGHT VISUALIZATION (T-38 TALON)

Axial Velocity (U): 100.00 m/s Vert. Vel. (w): 0.00 m/s Pitch Rate (q): 0.00 deg/s Pitch Angle (θ): 0.00 deg Altitude Dev. (h): 0.00 m

AXIAL VELOCITY PERTURBATION u(t)

VERTICAL VELOCITY PERTURBATION w(t)

PITCH RATE q(t)

PITCH ANGLE θ(t) & AoA α(t)

CONTROL INPUTS u(t)

SHORT PERIOD EIGENVALUES

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oscillatory pitch damping mode

PHUGOID EIGENVALUES

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slow energy exchange mode

SHORT PERIOD STATUS

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dynamic stability assessment

PHUGOID STATUS

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dynamic stability assessment

ⓘ Longitudinal Flight Dynamics & Modal Decomposition
The longitudinal motion of an aircraft is a 4th-order dynamic system modeled in state space as dx/dt = A x + B u, where the state vector is x = [u, w, q, θ]ᵀ. This system decomposes into two primary natural modes:
1. Short Period Mode: A fast, heavily damped pitch oscillation dominated by changes in vertical velocity w (or angle of attack) and pitch rate q.
2. Phugoid Mode: A slow, lightly damped speed/altitude oscillation dominated by exchanges of kinetic energy (velocity u) and potential energy (altitude / pitch angle θ).
By adjusting the sliders, the eigenvalue blocks in the modal space are updated. The physical matrix A is then reconstructed via the transformation matrix T representing a typical twin-engine interceptor aircraft: A = T · A_modal · T⁻¹.
The Eigenmode Initializer lets you set initial states corresponding directly to the eigenvector of a specific mode. When simulated, you will see a clean, uncoupled modal response (e.g. pure short period or phugoid oscillation).