Henriques, Pedro G.; Natário, José The rocket problem in general relativity. (English) Zbl 1256.83007 J. Optim. Theory Appl. 154, No. 2, 500-524 (2012). Summary: We derive the covariant optimality conditions for rocket trajectories in general relativity, with and without a bound on the magnitude of the proper acceleration. The resulting theory is then applied to solve two specific problems: the minimum fuel consumption transfer between two galaxies in a FLRW model, and between two stable circular orbits in the Schwarzschild spacetime. Cited in 1 ReviewCited in 1 Document MSC: 83C10 Equations of motion in general relativity and gravitational theory Keywords:relativistic rocket; optimal trajectory; general relativity; Friedmann-Lemaître-Robertson-Walker models; Schwarzschild solution; Hohmann manoeuvre PDFBibTeX XMLCite \textit{P. G. Henriques} and \textit{J. Natário}, J. Optim. Theory Appl. 154, No. 2, 500--524 (2012; Zbl 1256.83007) Full Text: DOI arXiv References: [1] Lawden, D.: Optimal Trajectories for Space Navigation. Butterworths, London (1963) · Zbl 0111.19605 [2] Natário, J.: Optimal time travel in the Gödel universe. Gen. Relativ. Gravit. 44, 855–874 (2012) · Zbl 1241.83018 [3] Misner, C., Thorne, K., Wheeler, J.A.: Gravitation. Freeman, New York (1973) [4] Ackeret, J.: Zur Theorie der Raketen. Helv. Phys. Acta 19, 103–112 (1946) [5] Seifert, H., Mills, M., Summerfield, M.: Physics of rockets: Dynamics of long range rockets. Am. J. Phys. 15, 255–272 (1947) [6] Bade, W.: Relativistic rocket theory. Am. J. Phys. 21, 310–312 (1953) [7] Rindler, W.: Hyperbolic motion in curved space time. Phys. Rev. 119, 2082–2089 (1960) · Zbl 0097.42403 [8] Burcev, P.: Meshchersky’s equations in the general theory of relativity. Bull. Astron. Inst. Czechoslov. 14, 124–127 (1962) · Zbl 0124.45103 [9] Rhee, J.: Relativistic rocket motion. Am. J. Phys. 33, 587–588 (1965) · Zbl 0137.45301 [10] Pomeranz, K.: The relativistic rocket. Am. J. Phys. 34, 565–566 (1966) [11] Mesterton-Gibbons, M.: A Primer on the Calculus of Variations and Optimal Control Theory. American Mathematical Society, Providence (2009) · Zbl 1225.49001 [12] Arutyunov, A., Karamzin, D., Pereira, F.: On a generalization of the impulsive control concept: controlling system jumps. Discrete Contin. Dyn. Syst. 29, 403–415 (2011) · Zbl 1209.49048 [13] Hohmann, W.: Die Erreichbarkeit der Himmelskörper. Oldenbourg, Munich (1925) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.