Mathematics
Scientific paper
May 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979phdt.........3l&link_type=abstract
Ph.D. Thesis Michigan Univ., Ann Arbor.
Mathematics
Atmospheric Entry, Orbit Decay, Orbital Mechanics, Spacecraft Orbits, Aerodynamic Drag, Equations Of Motion, Mathematical Models, Planetary Landing
Scientific paper
Equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipative force of drag through the dynamic phase of reentry and finally to the point of contact with the planetary surface. A complete uniformly valid theory is developed for orbit contraction due to atmospheric drag for all elliptic orbits in the case of orbital motion. A simple model is chosen in which the atmospheric density is assumed to vary exponentially with altitude. The universal entry equations applied to the problem of ballistic entry are described. The analytic theory of ballistic entry is developed by analyzing the three typical cases: (1) entry from a decaying orbit, (2) entry with circular speed at small initial flight path angles and (3) entry at moderate and large initial flight path angles with arbitrary speed. The second order theory is developed by applying Poincare's method of small parameters to a system of nonlinear equations.
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