Swing Equation

A second‑order differential equation that describes the rotational dynamics of a synchronous machine’s rotor angle and speed relative to a synchronously rotating reference frame, commonly written M d^2δ/dt^2 + D dδ/dt = Tm − Te where δ is rotor angle, M (or H) is the inertia‑related coefficient, D is a damping coefficient (frequency‑dependent damping may be represented), Tm is mechanical torque (o