The phugoid is a relatively low-frequency oscillation in which kinetic and potential energies are exchanged. The mode is generally characterized by low damping and approximately constant incidence: i.e. C_{L} and C_{D} both constant. In the following simplified analysis, it is assumed that the aircraft is initially trimmed straight-and-level at a horizontal speed V_{0}. Lift and weight balance, as do thrust and drag.
We now assume that the velocity vector is perturbed from V=(V_{0}, 0) to V=(V_{0}+u, w) where u and w are small (relative to V_{0}) perturbations in the x and z directions in the inertial (i.e. non-rotating and non-accelerating) axis system o_{xz}. Using a local tangent approximation to the quadratic dependency of lift and drag on speed, the lift and drag will increase by small increments