NASA, Optimal Guidance Law Development for an Advanced Launch System by Anthony J. Calise and Martin S. K. Leung Georgia Institute of Technology, Atlanta, Georgia, 1995

NASA, Optimal Guidance Law Development for an Advanced Launch System by Anthony J. Calise and Martin S. K. Leung Georgia Institute of Technology, Atlanta, Georgia, 1995,

The following quotations demonstrate that the primary model used in this document is Flat Earth. That is not to say the document does not also contain considerations of spherical earth which it does contain.

“In [2], Chandler and Smith have developed an IGM for the Saturn V vehicle. It is based on a flat Earth no-atmosphere model, and is further simplified with linear angle steering guidance.”

(Pg. 2)

“In [13], Jacobson and Powers have developed an explicit guidance scheme also for low thrust space flight. It is basically a retargeting procedure and uses an analytic solution for the inertially fixed and constant acceleration flight. Recently, Feeley and Speyer [14] have used regular perturbations on the expansion of the Hamilton-Jacobi-Bellman (HJB) equation, and have applied it to the launch vehicle guidance problem for exoatmospheric flight. The approach requires an analytic zero order solution and quadrature evaluation. The analytic solution is again based on a flat Earth, no-atmosphere approximation, and the neglected dynamics are introduced as perturbations.”

(Pg. 3)

“Sec. 2 presents the formulation of the launch vehicle trajectory optimization problem, which includes the equations of motion and the vehicle aerodynamic and propulsion models that are based on a generic model of the ALS. The results for two purely analytical approaches are documented in Sec. 3. The first is a singular perturbation approach using an energy state approximation and a 2-state model. The second is a regular perturbation approach based on the zero order solution for a flat Earth no-atmosphere assumption.”

(Pg. 4)

“Assuming that the dominant forces on the launch vehicle are thrust and gravity, an attempt is made to treat the atmospheric effects as a perturbation effect. To further simplify the problem, spherical Earth effects are also considered as perturbations (these effects are only apparent when the vehicle reaches orbital speed near the end of the flight). The result is similar to the maximum horizontal speed transfer problem in [33] for a flat Earth no atmosphere situation.”

(Pg. 33)

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950019785.pdf

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