PHUGOID MOTION FOR GRAZING-ENTRY TRAJECTORIES AT NEAR-CIRCULAR SPEEDS

We analyze the trajectory perturbations that result in phugoid oscilla tions during the grazing planetary entry of space vehicles starting wi th near-circular speed, in ballistic and equilibrium glide modes. The equations for planar entry are transformed into a dimensionless system appropriate for an analytical integration that provides accurate resu lts in comparison with those obtained from a numerical integration of the original system. For ballistic entry, the small perturbation in th e flight-path angle is a lightly damped oscillation with long period, while the perturbation in the density (altitude) increases as the spee d decreases. Nevertheless, the relative change in the density is decre asing, and the phugoid in ballistic entry is termed stable in both the Right-path angle and the altitude. For glide entry, in the reference solution where there is equilibrium of forces along the normal to the flight path, both the flight-path angle and the altitude have a steady decrease along the Right path. With a slight perturbation in either t he initial speed or the initial Right-path angle, or both, the traject ory variables undergo a damped oscillation about the reference traject ory, Both the damping and the frequency are obtained explicitly, and t hey correctly predict the phugoid motion as seen in the numerical solu tion.