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. CL and CD 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 oxz. Using a local tangent approximation to the quadratic dependency of lift and drag on speed, the lift and drag will increase by small increments