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 V₀. Lift and weight balance, as do thrust and drag.

We now assume that the velocity vector is perturbed from V=(V₀, 0) to V=(V₀+u, w) where u and w are small (relative to V₀) 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