Topic
Goddard problem
About: Goddard problem is a research topic. Over the lifetime, 13 publications have been published within this topic receiving 153 citations.
Papers
TL;DR: In this article, the effects of two additional constraints, namely, a dynamic pressure limit and specified final time, were dealt with, and a simple intuitive feedback law was presented for the free time problem.
Abstract: The Goddard problem is that of maximizing the final altitude for a vertically ascending, rocket-powered vehicle under the influence of an inverse square gravitational field and atmospheric drag. The present paper deals with the effects of two additional constraints, namely, a dynamic pressure limit and specified final time. Nine different switching structures involving zero-thrust arcs, full-thrust arcs, singular-thrust arcs, and state-constrained arcs are obtained when the value of the dynamic pressure limit is varied between zero and infinity and the final time is specified between the minimum possible time within which all of the fuel can be burned and the natural final time that emerges for the problem with final time unspecified. For all points in the aforementioned domain of dynamic pressure limit and prescribed final time, the associated optimal switching structure is clearly identified. Finally, a simple intuitive feedback law is presented for the free time problem. For all values of prescribed dynamic pressure limit, this strategy yields a loss in final altitude of less than 3 percent with respect to the associated optimal solution.
60 citations
TL;DR: Analysis shows the possibility of a more complex switching structure than the classical full-singular-coast sequence, with the appearance of a second full-thrust subarc in the transition from the subsonic to the supersonic region.
37 citations
TL;DR: In this paper, the authors address the well-known Goddard problem in the formulation of Seywald and Cliff with the objective to maximize the altitude of a vertically ascending rocket subject to dynamic pressure and thrust constraints.
33 citations
30 citations
TL;DR: In this article, the problem of optimizing the thrust of a vertically ascending rocket is solved under the assumption of isothermal atmosphere in two important cases: 1) the jet Mach number and the fuel supply are sufficiently large; 2) the drag is a convex function of the velocity.
Abstract: The problem of optimizing the thrust of a vertically ascending rocket is solved here under the assumption of isothermal atmosphere in two important cases: 1) the jet Mach number and the fuel supply are sufficiently large; 2) the drag is a convex function of the velocityThe first case embraces all physical drags and is valid for the Earth; the second extends to all atmospheres, but is restricted to drags that arc fairly commonWith impulsive boosts in velocity admitted, the solution is shown to contain a finite number of such boosts in the sonic region of the rocket velocity, and to contain no coasting arcs except in the terminal stageAn absolute minimum is proved with the aid of a sufficient condition applicable to problems of optimum control
21 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 2 |
| 2017 | 1 |
| 2014 | 1 |
| 2008 | 1 |
| 1993 | 1 |
| 1992 | 1 |