The gravitational accelerations acting on a flight vehicle caused by a planetary body can be modeled very accurately using the Legendre polynomial functions. However the gravity harmonic coefficients for the Legendre polynomials are not that easy to determined and must be solved for beforehand by using tracking data measurements from a known space vehicle in orbit around the planet. This method to model real world gravitational environments is applied in many aerospace vehicle motion simulations.

The Earth s atmosphere can be modeled accurately to an altitude of about 86 kilometers by using the perfect gas law and the hydrostatic equation for both temperature and density. Above 86 kilometers however, the total atmospheric molecular weight varies, and density and temperature become functions of a number of parameters, such as solar and geomagnetic activity. In these high altitude regions of the atmosphere, dynamic atmosphere models, such as that offered by L. G. Jacchia, must be used to estimate the temperature and density environments.

I have introduced the reader to some of the fundamentals for computing the fluid dynamic forces and moments on the flight vehicle using finite element modeling techniques. These methods began to be develop after 1965 as the aerodynamist had access to more computing power.

I have outlined the use of Cowell s solution methods and the techniques for the numerical solution of the six-DOF airframe motion applied in actual GNC flight simulators. This simulation method can use many of the acceleration, force, and moment models presented in this chapter to...