{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T18:33:07Z","timestamp":1777314787677,"version":"3.51.4"},"reference-count":98,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s10957-021-01884-1","type":"journal-article","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T14:02:50Z","timestamp":1626271370000},"page":"634-674","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Unconstrained Direct Optimization of Spacecraft Trajectories Using Many Embedded Lambert Problems"],"prefix":"10.1007","volume":"191","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3254-6759","authenticated-orcid":false,"given":"David","family":"Ottesen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryan P.","family":"Russell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"issue":"2","key":"1884_CR1","doi-asserted-by":"publisher","first-page":"456","DOI":"10.2514\/1.24701","volume":"44","author":"O Abdelkhalik","year":"2007","unstructured":"Abdelkhalik, O., Mortari, D.: N-impulse orbit transfer using genetic algorithms. J. Spacecr. Rocket. 44(2), 456\u2013460 (2007). https:\/\/doi.org\/10.2514\/1.24701","journal-title":"J. Spacecr. Rocket."},{"issue":"5","key":"1884_CR2","doi-asserted-by":"publisher","first-page":"962","DOI":"10.2514\/1.A32307","volume":"49","author":"O Abdelkhalik","year":"2012","unstructured":"Abdelkhalik, O., Taheri, E.: Approximate on-off low-thrust space trajectories using Fourier series. J. Spacecr. Rocket. 49(5), 962\u2013965 (2012). https:\/\/doi.org\/10.2514\/1.A32307","journal-title":"J. Spacecr. Rocket."},{"key":"1884_CR3","unstructured":"Arora, N., Russell, R.P.: A fast and robust multiple revolution lambert algorithm using a cosine transformation. In: AAS\/AIAA Astrodynamics Specialist Conference, AAS 13-728. Springfield, VA (2013)"},{"issue":"9","key":"1884_CR4","doi-asserted-by":"publisher","first-page":"1563","DOI":"10.2514\/1.G001030","volume":"38","author":"N Arora","year":"2015","unstructured":"Arora, N., Russell, R.P., Strange, N., Ottesen, D.: Partial derivatives of the solution to the lambert boundary value problem. J. Guid. Control Dyn. 38(9), 1563\u20131572 (2015). https:\/\/doi.org\/10.2514\/1.G001030","journal-title":"J. Guid. Control Dyn."},{"key":"1884_CR5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971231","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Mattheij, R.M., Russell, R.D.: Numerical solution of boundary value problems for ordinary differential equations. SIAM (1995). https:\/\/doi.org\/10.1137\/1.9781611971231","journal-title":"SIAM"},{"issue":"3","key":"1884_CR6","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1119\/1.1934788","volume":"27","author":"RH Bacon","year":"1959","unstructured":"Bacon, R.H.: Logarithmic spiral: an ideal trajectory for the interplanetary vehicle with engines of low sustained thrust. Am. J. Phys. 27(3), 164\u2013165 (1959). https:\/\/doi.org\/10.1119\/1.1934788","journal-title":"Am. J. Phys."},{"issue":"1","key":"1884_CR7","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/BF01258313","volume":"9","author":"CA Balafoutis","year":"1994","unstructured":"Balafoutis, C.A.: A survey of efficient computational methods for manipulator inverse dynamics. J. Intell. Rob. Syst. 9(1), 45\u201371 (1994). https:\/\/doi.org\/10.1007\/BF01258313","journal-title":"J. Intell. Rob. Syst."},{"issue":"5","key":"1884_CR8","doi-asserted-by":"publisher","first-page":"707","DOI":"10.2514\/3.60680","volume":"15","author":"RH Battin","year":"1977","unstructured":"Battin, R.H.: Lambert\u2019s problem revisited. AIAA J. 15(5), 707\u2013713 (1977). https:\/\/doi.org\/10.2514\/3.60680","journal-title":"AIAA J."},{"key":"1884_CR9","doi-asserted-by":"publisher","unstructured":"Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics, revised edn. AIAA Education Series. American Institute of Aeronautics and Astronautics, Reston (1999). https:\/\/doi.org\/10.2514\/4.861543","DOI":"10.2514\/4.861543"},{"issue":"2","key":"1884_CR10","doi-asserted-by":"publisher","first-page":"193","DOI":"10.2514\/2.4231","volume":"21","author":"JT Betts","year":"1998","unstructured":"Betts, J.T.: Survey of numerical methods for trajectory optimization. J. Guid. Control Dyn. 21(2), 193\u2013207 (1998). https:\/\/doi.org\/10.2514\/2.4231","journal-title":"J. Guid. Control Dyn."},{"issue":"2","key":"1884_CR11","doi-asserted-by":"publisher","first-page":"431","DOI":"10.2514\/3.20656","volume":"14","author":"JT Betts","year":"1991","unstructured":"Betts, J.T., Huffman, W.P.: Trajectory optimization on a parallel processor. J. Guid. Control Dyn. 14(2), 431\u2013439 (1991). https:\/\/doi.org\/10.2514\/3.20656","journal-title":"J. Guid. Control Dyn."},{"key":"1884_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/s40295-018-00146-z","author":"KA Bokelmann","year":"2019","unstructured":"Bokelmann, K.A., Russell, R.P.: Optimization of impulsive Europa capture trajectories using primer vector theory. J. Astronaut. Sci. (2019). https:\/\/doi.org\/10.1007\/s40295-018-00146-z","journal-title":"J. Astronaut. Sci."},{"issue":"2","key":"1884_CR13","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s10883-008-9040-1","volume":"14","author":"B Bonnard","year":"2008","unstructured":"Bonnard, B., Janin, G.: Geometric orbital transfer using averaging techniques. J. Dyn. Control Syst. 14(2), 145\u2013167 (2008). https:\/\/doi.org\/10.1007\/s10883-008-9040-1","journal-title":"J. Dyn. Control Syst."},{"issue":"4","key":"1884_CR14","doi-asserted-by":"publisher","first-page":"1197","DOI":"10.2514\/1.49449","volume":"34","author":"G Boyarko","year":"2011","unstructured":"Boyarko, G., Romano, M., Yakimenko, O.: Time-optimal reorientation of a spacecraft using an inverse dynamics optimization method. J. Guid. Control Dyn. 34(4), 1197\u20131208 (2011). https:\/\/doi.org\/10.2514\/1.49449","journal-title":"J. Guid. Control Dyn."},{"issue":"1","key":"1884_CR15","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1093\/imamat\/6.1.76","volume":"6","author":"CG Broyden","year":"1970","unstructured":"Broyden, C.G.: The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA J. Appl. Math. 6(1), 76\u201390 (1970). https:\/\/doi.org\/10.1093\/imamat\/6.1.76","journal-title":"IMA J. Appl. Math."},{"key":"1884_CR16","doi-asserted-by":"publisher","unstructured":"Buffington, B.: Trajectory design concept for the proposed europa clipper mission. In: AAS\/AIAA Astrodynamics Specialist Conference, 2014-4105. San Diego, CA (2014). https:\/\/doi.org\/10.2514\/6.2014-4105","DOI":"10.2514\/6.2014-4105"},{"key":"1884_CR17","doi-asserted-by":"publisher","unstructured":"Buffington, B., Strange, N., Smith, J.: Overview of the cassini extended mission trajectory. In: AAS\/AIAA Astrodynamics Specialist Conference and Exhibit, AIAA 2008-6752. Honolulu, Hawaii (2008). https:\/\/doi.org\/10.2514\/6.2008-6752","DOI":"10.2514\/6.2008-6752"},{"issue":"1\u20133","key":"1884_CR18","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF01582063","volume":"63","author":"RH Byrd","year":"1994","unstructured":"Byrd, R.H., Nocedal, J., Schnabel, R.B.: Representations of quasi-newton matrices and their use in limited memory methods. Math. Program. 63(1\u20133), 129\u2013156 (1994). https:\/\/doi.org\/10.1007\/BF01582063","journal-title":"Math. Program."},{"issue":"2","key":"1884_CR19","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s10957-011-9918-z","volume":"152","author":"BA Conway","year":"2012","unstructured":"Conway, B.A.: A survey of methods available for the numerical optimization of continuous dynamic systems. J. Optim. Theory Appl. 152(2), 271\u2013306 (2012). https:\/\/doi.org\/10.1007\/s10957-011-9918-z","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"1884_CR20","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1109\/99.660313","volume":"5","author":"L Dagum","year":"1998","unstructured":"Dagum, L., Menon, R.: Openmp: an industry standard API for shared-memory programming. Comput. Sci. Eng. IEEE 5(1), 46\u201355 (1998)","journal-title":"Comput. Sci. Eng. IEEE"},{"issue":"1\u20134","key":"1884_CR21","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/BF00216849","volume":"60","author":"LA D\u2019Amario","year":"1992","unstructured":"D\u2019Amario, L.A., Bright, L.E., Wolf, A.A.: Galileo trajectory design. Space Sci. Rev. 60(1\u20134), 23\u201378 (1992). https:\/\/doi.org\/10.1007\/BF00216849","journal-title":"Space Sci. Rev."},{"key":"1884_CR22","unstructured":"D\u2019Amario, L.A., Byrnes, D.V., Sackett, L.L., Stanford, R.H.: Optimization of multiple flyby trajectories. Provincetown, MA (1979). https:\/\/ntrs.nasa.gov\/search.jsp?R=19790063226. Accessed 1 May 2017"},{"issue":"5","key":"1884_CR23","doi-asserted-by":"publisher","first-page":"591","DOI":"10.2514\/3.56115","volume":"4","author":"LA D\u2019Amario","year":"1981","unstructured":"D\u2019Amario, L.A., Byrnes, D.V., Stanford, R.H.: A new method for optimizing multiple-flyby trajectories. J. Guid. Control Dyn. 4(5), 591\u2013596 (1981). https:\/\/doi.org\/10.2514\/3.56115","journal-title":"J. Guid. Control Dyn."},{"issue":"4","key":"1884_CR24","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s10569-008-9170-5","volume":"102","author":"P Di Lizia","year":"2008","unstructured":"Di Lizia, P., Armellin, R., Lavagna, M.: Application of high order expansions of two-point boundary value problems to astrodynamics. Celest. Mech. Dyn. Astron. 102(4), 355\u2013375 (2008). https:\/\/doi.org\/10.1007\/s10569-008-9170-5","journal-title":"Celest. Mech. Dyn. Astron."},{"issue":"3","key":"1884_CR25","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s10569-010-9327-x","volume":"109","author":"KE Davis","year":"2011","unstructured":"Davis, K.E., Anderson, R.L., Scheeres, D.J., Born, G.H.: Optimal transfers between unstable periodic orbits using invariant manifolds. Celest. Mech. Dyn. Astron. 109(3), 241\u2013264 (2011). https:\/\/doi.org\/10.1007\/s10569-010-9327-x","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"1884_CR26","doi-asserted-by":"publisher","unstructured":"Fang, Q., Wang, X., Sun, C., Yuan, J.: A shape-based method for continuous low-thrust trajectory design between circular coplanar orbits. Int. J. Aerosp. Eng. (2017). https:\/\/doi.org\/10.1155\/2017\/9234905","DOI":"10.1155\/2017\/9234905"},{"issue":"3","key":"1884_CR27","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1093\/comjnl\/13.3.317","volume":"13","author":"R Fletcher","year":"1970","unstructured":"Fletcher, R.: A new approach to variable metric algorithms. Comput. J. 13(3), 317\u2013322 (1970). https:\/\/doi.org\/10.1093\/comjnl\/13.3.317","journal-title":"Comput. J."},{"issue":"2","key":"1884_CR28","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1093\/comjnl\/7.2.149","volume":"7","author":"R Fletcher","year":"1964","unstructured":"Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. Comput. J. 7(2), 149\u2013154 (1964). https:\/\/doi.org\/10.1093\/comjnl\/7.2.149","journal-title":"Comput. J."},{"key":"1884_CR29","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.actaastro.2019.05.050","volume":"168","author":"R Furfaro","year":"2020","unstructured":"Furfaro, R., Mortari, D.: Least-squares solution of a class of optimal space guidance problems via theory of connections. Acta Astronaut. 168, 92\u2013103 (2020). https:\/\/doi.org\/10.1016\/j.actaastro.2019.05.050","journal-title":"Acta Astronaut."},{"key":"1884_CR30","doi-asserted-by":"publisher","unstructured":"Gao, Y., Kluever, C.: Low-thrust interplanetary orbit transfers using hybrid trajectory optimization method with multiple shooting. In: AIAA\/AAS Astrodynamics Specialist Conference and Exhibit, AIAA 2004-5088. Providence, RI (2004). https:\/\/doi.org\/10.2514\/6.2004-5088","DOI":"10.2514\/6.2004-5088"},{"issue":"6","key":"1884_CR31","doi-asserted-by":"publisher","first-page":"1320","DOI":"10.2514\/1.14698","volume":"28","author":"Y Gao","year":"2005","unstructured":"Gao, Y., Kluever, C.: Analytic orbital averaging technique for computing tangential-thrust trajectories. J. Guid. Control Dyn. 28(6), 1320\u20131323 (2005). https:\/\/doi.org\/10.2514\/1.14698","journal-title":"J. Guid. Control Dyn."},{"issue":"3","key":"1884_CR32","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/S0094-5765(97)00208-7","volume":"41","author":"S Geffroy","year":"1997","unstructured":"Geffroy, S., Epenoy, R.: Optimal low-thrust transfers with constraints-generalization of averaging techniques. Acta Astronaut. 41(3), 133\u2013149 (1997). https:\/\/doi.org\/10.1016\/S0094-5765(97)00208-7","journal-title":"Acta Astronaut."},{"issue":"1","key":"1884_CR33","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1137\/S0036144504446096","volume":"47","author":"PE Gill","year":"2005","unstructured":"Gill, P.E., Murray, W., Saunders, M.A.: Snopt: an sqp algorithm for large-scale constrained optimization. SIAM 47(1), 99\u2013132 (2005). https:\/\/doi.org\/10.1137\/S0036144504446096","journal-title":"SIAM"},{"issue":"2","key":"1884_CR34","doi-asserted-by":"publisher","first-page":"363","DOI":"10.2514\/3.5109","volume":"7","author":"DR Glandorf","year":"1969","unstructured":"Glandorf, D.R.: Lagrange multipliers and the state transition matrix for coasting arcs. AIAA J. 7(2), 363\u2013365 (1969). https:\/\/doi.org\/10.2514\/3.5109","journal-title":"AIAA J."},{"issue":"109","key":"1884_CR35","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1090\/S0025-5718-1970-0258249-6","volume":"24","author":"D Goldfarb","year":"1970","unstructured":"Goldfarb, D.: A family of variable-metric methods derived by variational means. Math. Comput. 24(109), 23\u201326 (1970). https:\/\/doi.org\/10.1090\/S0025-5718-1970-0258249-6","journal-title":"Math. Comput."},{"key":"1884_CR36","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/BF00049511","volume":"48","author":"RH Gooding","year":"1990","unstructured":"Gooding, R.H.: A procedure for the solution of Lambert\u2019s orbital boundary-value problem. Celest. Mech. Dyn. Astron. 48, 145\u2013165 (1990). https:\/\/doi.org\/10.1007\/BF00049511","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"1884_CR37","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1086\/109713","volume":"70","author":"WH Goodyear","year":"1965","unstructured":"Goodyear, W.H.: Completely general closed-form solution for coordinates and partial derivative of the two-body problem. Astron. J. 70, 189 (1965). https:\/\/doi.org\/10.1086\/109713","journal-title":"Astron. J."},{"issue":"3","key":"1884_CR38","doi-asserted-by":"publisher","first-page":"711","DOI":"10.2514\/1.A33187","volume":"52","author":"KF Graham","year":"2015","unstructured":"Graham, K.F., Rao, A.V.: Minimum-time trajectory optimization of multiple revolution low-thrust earth-orbit transfers. J. Spacecr. Rocket. 52(3), 711\u2013727 (2015). https:\/\/doi.org\/10.2514\/1.A33187","journal-title":"J. Spacecr. Rocket."},{"issue":"2","key":"1884_CR39","doi-asserted-by":"publisher","first-page":"289","DOI":"10.2514\/1.A33416","volume":"53","author":"KF Graham","year":"2016","unstructured":"Graham, K.F., Rao, A.V.: Minimum-time trajectory optimization of low-thrust earth-orbit transfers with eclipsing. J. Spacecr. Rocket. 53(2), 289\u2013303 (2016). https:\/\/doi.org\/10.2514\/1.A33416","journal-title":"J. Spacecr. Rocket."},{"issue":"6","key":"1884_CR40","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.2514\/1.4022","volume":"27","author":"T Haberkorn","year":"2004","unstructured":"Haberkorn, T., Martinon, P., Gergaud, J.: Low-thrust minimum-fuel orbital transfer: a homotopic approach. J. Guid. Control Dyn. 27(6), 1046\u20131060 (2004). https:\/\/doi.org\/10.2514\/1.4022","journal-title":"J. Guid. Control Dyn."},{"issue":"1","key":"1884_CR41","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/030601880","volume":"16","author":"WW Hager","year":"2005","unstructured":"Hager, W.W., Zhang, H.: A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16(1), 170\u2013192 (2005). https:\/\/doi.org\/10.1137\/030601880","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1884_CR42","first-page":"35","volume":"2","author":"WW Hager","year":"2006","unstructured":"Hager, W.W., Zhang, H.: A survey of nonlinear conjugate gradient methods. Pac. J. Optim. 2(1), 35\u201358 (2006)","journal-title":"Pac. J. Optim."},{"key":"1884_CR43","unstructured":"Hatten, N., Russell, R.P.: Application of the stark problem to space trajectories with time-varying perturbations. In: AAS\/AIAA Astrodynamics Specialist Conference. AAS 14\u2013230, vol. 152, pp. 439\u2013457. Santa Fe, NM (2014)"},{"issue":"4","key":"1884_CR44","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/BF00692008","volume":"58","author":"LA Hiday-Johnston","year":"1994","unstructured":"Hiday-Johnston, L.A., Howell, K.C.: Transfers between libration-point orbits in the elliptic restricted problem. Celest. Mech. Dyn. Astron. 58(4), 317\u2013337 (1994). https:\/\/doi.org\/10.1007\/BF00692008","journal-title":"Celest. Mech. Dyn. Astron."},{"issue":"5","key":"1884_CR45","doi-asserted-by":"publisher","first-page":"1242","DOI":"10.2514\/1.21796","volume":"29","author":"D Izzo","year":"2006","unstructured":"Izzo, D.: Lambert\u2019s problem for exponential sinusoids. J. Guid. Control Dyn. 29(5), 1242\u20131245 (2006). https:\/\/doi.org\/10.2514\/1.21796","journal-title":"J. Guid. Control Dyn."},{"issue":"1","key":"1884_CR46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10569-014-9587-y","volume":"121","author":"D Izzo","year":"2015","unstructured":"Izzo, D.: Revisiting Lambert\u2019s problem. Celest. Mech. Dyn. Astron. 121(1), 1\u201315 (2015). https:\/\/doi.org\/10.1007\/s10569-014-9587-y","journal-title":"Celest. Mech. Dyn. Astron."},{"issue":"2","key":"1884_CR47","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s10898-006-9106-0","volume":"38","author":"D Izzo","year":"2007","unstructured":"Izzo, D., Becerra, V.M., Myatt, D.R., Nasuto, S.J., Bishop, J.M.: Search space pruning and global optimisation of multiple gravity assist spacecraft trajectories. J. Glob. Optim. 38(2), 283\u2013296 (2007). https:\/\/doi.org\/10.1007\/s10898-006-9106-0","journal-title":"J. Glob. Optim."},{"key":"1884_CR48","unstructured":"Jezewski, D.J.: Primer vector theory and applications. Tech. rep., Technical Report NASA TR R-454, Lyndon B Johnson Space Center, Houston, Texas, 77058 (1975). https:\/\/ntrs.nasa.gov\/search.jsp?R=19760004112"},{"issue":"4","key":"1884_CR49","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1002\/oca.4660010408","volume":"1","author":"DJ Jezewski","year":"1980","unstructured":"Jezewski, D.J.: Primer vector theory applied to the linear relative-motion equations. Optim. Control Appl. Methods 1(4), 387\u2013401 (1980). https:\/\/doi.org\/10.1002\/oca.4660010408","journal-title":"Optim. Control Appl. Methods"},{"issue":"11","key":"1884_CR50","doi-asserted-by":"publisher","first-page":"2160","DOI":"10.2514\/3.4949","volume":"6","author":"DJ Jezewski","year":"1968","unstructured":"Jezewski, D.J., Rozendaal, H.L.: An efficient method for calculating optimal free-space n-impulse trajectories. AIAA J. 6(11), 2160\u20132165 (1968). https:\/\/doi.org\/10.2514\/3.4949","journal-title":"AIAA J."},{"key":"1884_CR51","unstructured":"Jones, B.A., Anderson, R.L.: A survey of symplectic and collocation integration methods for orbit propagation. In: 22nd Annual AAS\/AIAA Space Flight Mechanics Meeting, AAS 12-214. Charleston, SC (2012). https:\/\/ntrs.nasa.gov\/search.jsp?R=20130000293"},{"issue":"1\u20132","key":"1884_CR52","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/BF03321509","volume":"57","author":"JA K\u00e9chichian","year":"2009","unstructured":"K\u00e9chichian, J.A.: Optimal low-thrust transfer in general circular orbit using analytic averaging of the system dynamics. J. Astronaut. Sci. 57(1\u20132), 369\u2013392 (2009). https:\/\/doi.org\/10.1007\/BF03321509","journal-title":"J. Astronaut. Sci."},{"issue":"2","key":"1884_CR53","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/BF00200846","volume":"21","author":"CE Kohlhase","year":"1977","unstructured":"Kohlhase, C.E., Penzo, P.A.: Voyager mission description. Space Sci. Rev. 21(2), 77\u2013101 (1977). https:\/\/doi.org\/10.1007\/BF00200846","journal-title":"Space Sci. Rev."},{"issue":"7","key":"1884_CR54","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.2514\/1.G003172","volume":"41","author":"D Landau","year":"2018","unstructured":"Landau, D.: Efficient maneuver placement for automated trajectory design. J. Guid. Control Dyn. 41(7), 1531\u20131541 (2018). https:\/\/doi.org\/10.2514\/1.G003172","journal-title":"J. Guid. Control Dyn."},{"issue":"2","key":"1884_CR55","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1007\/s10957-012-0039-0","volume":"154","author":"G Lantoine","year":"2012","unstructured":"Lantoine, G., Russell, R.P.: A hybrid differential dynamic programming algorithm for constrained optimal control problems. Part 1: Theory. J. Optim. Theory Appl. 154(2), 382\u2013417 (2012). https:\/\/doi.org\/10.1007\/s10957-012-0039-0","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"1884_CR56","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1007\/s10957-012-0038-1","volume":"154","author":"G Lantoine","year":"2012","unstructured":"Lantoine, G., Russell, R.P.: A hybrid differential dynamic programming algorithm for constrained optimal control problems. Part 2: Application. J. Optim. Theory Appl. 154(2), 418\u2013442 (2012). https:\/\/doi.org\/10.1007\/s10957-012-0038-1","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"1884_CR57","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1145\/355841.355847","volume":"5","author":"CL Lawson","year":"1979","unstructured":"Lawson, C.L., Hanson, R.J., Kincaid, D.R., Krogh, F.T.: Basic linear algebra subprograms for fortran usage. ACM Trans. Math. Softw. 5(3), 308\u2013323 (1979). https:\/\/doi.org\/10.1145\/355841.355847","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"1884_CR58","doi-asserted-by":"publisher","first-page":"127","DOI":"10.2514\/3.4452","volume":"6","author":"PM Lion","year":"1968","unstructured":"Lion, P.M., Handelsman, M.: Primer vector on fixed-time impulsive trajectories. AIAA J. 6(1), 127\u2013132 (1968). https:\/\/doi.org\/10.2514\/3.4452","journal-title":"AIAA J."},{"issue":"4","key":"1884_CR59","doi-asserted-by":"publisher","first-page":"726","DOI":"10.2514\/3.21073","volume":"16","author":"P Lu","year":"1993","unstructured":"Lu, P.: Inverse dynamics approach to trajectory optimization for an aerospace plane. J. Guid. Control Dyn. 16(4), 726\u2013732 (1993). https:\/\/doi.org\/10.2514\/3.21073","journal-title":"J. Guid. Control Dyn."},{"issue":"1","key":"1884_CR60","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.actaastro.2013.07.018","volume":"94","author":"AE Lynam","year":"2014","unstructured":"Lynam, A.E.: Broad-search algorithms for the spacecraft trajectory design of Callisto\u2013Ganymede\u2013Io triple flyby sequences from 2024 to 2040, part i: Heuristic pruning of the search space. Acta Astronaut. 94(1), 246\u2013252 (2014). https:\/\/doi.org\/10.1016\/j.actaastro.2013.07.018","journal-title":"Acta Astronaut."},{"issue":"1","key":"1884_CR61","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/j.actaastro.2013.07.020","volume":"94","author":"AE Lynam","year":"2014","unstructured":"Lynam, A.E.: Broad-search algorithms for the spacecraft trajectory design of Callisto\u2013Ganymede\u2013Io triple flyby sequences from 2024 to 2040, part ii: Lambert pathfinding and trajectory solutions. Acta Astronaut. 94(1), 253\u2013261 (2014). https:\/\/doi.org\/10.1016\/j.actaastro.2013.07.020","journal-title":"Acta Astronaut."},{"issue":"4","key":"1884_CR62","doi-asserted-by":"publisher","first-page":"884","DOI":"10.2514\/1.27205","volume":"44","author":"BG Marchand","year":"2007","unstructured":"Marchand, B.G., Howell, K.C., Wilson, R.S.: Improved corrections process for constrained trajectory design in the n-body problem. J. Spacecr. Rocket. 44(4), 884\u2013897 (2007). https:\/\/doi.org\/10.2514\/1.27205","journal-title":"J. Spacecr. Rocket."},{"key":"1884_CR63","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-41812-8.50005-3","volume-title":"Optimal Space Trajectories","author":"JP Marec","year":"1979","unstructured":"Marec, J.P.: Optimal Space Trajectories, vol. 1. Elsevier, New York (1979)"},{"issue":"5","key":"1884_CR64","doi-asserted-by":"publisher","first-page":"1054","DOI":"10.2514\/1.18178","volume":"43","author":"JV McAdams","year":"2006","unstructured":"McAdams, J.V., Dunham, D.W., Farquhar, R.W., Taylor, A.H., Williams, B.G.: Trajectory design and maneuver strategy for the messenger mission to mercury. J. Spacecr. Rocket. 43(5), 1054\u20131064 (2006). https:\/\/doi.org\/10.2514\/1.18178","journal-title":"J. Spacecr. Rocket."},{"issue":"4","key":"1884_CR65","doi-asserted-by":"publisher","first-page":"57","DOI":"10.3390\/math5040057","volume":"5","author":"D Mortari","year":"2017","unstructured":"Mortari, D.: The theory of connections: connecting points. Mathematics 5(4), 57 (2017). https:\/\/doi.org\/10.3390\/math5040057","journal-title":"Mathematics"},{"key":"1884_CR66","unstructured":"NASA Planetary Data System: Cassini\u2013Huygens Mission Information. Accessed Mar. 3, 2021. https:\/\/pds.nasa.gov\/ds-view\/pds\/viewMissionProfile.jsp?MISSION_NAME=CASSINI-HUYGENS"},{"issue":"1","key":"1884_CR67","doi-asserted-by":"publisher","first-page":"128","DOI":"10.2514\/1.50434","volume":"34","author":"DM Novak","year":"2011","unstructured":"Novak, D.M., Vasile, M.: Improved shaping approach to the preliminary design of low-thrust trajectories. J. Guid. Control Dyn. 34(1), 128\u2013147 (2011). https:\/\/doi.org\/10.2514\/1.50434","journal-title":"J. Guid. Control Dyn."},{"key":"1884_CR68","unstructured":"Ottesen, D., Russell, R.P.: Space trajectory optimization using embedded boundary value problems. In: AAS\/AIAA Astrodynamics Specialist Conference. AAS 17\u2013837, vol. 162, pp. 2271\u20132290. Stevenson, WA (2017)"},{"key":"1884_CR69","unstructured":"Ottesen, D., Russell, R.P.: A piecewise-constant sundman transformation for spacecraft trajectory optimization. In: AAS\/AIAA Astrodynamics Specialist Conference. AAS 18\u2013467, vol. 167, pp. 1755\u20131774. Snowbird, WA (2018)"},{"issue":"5","key":"1884_CR70","doi-asserted-by":"publisher","first-page":"1065","DOI":"10.2514\/1.19646","volume":"43","author":"PD Pascale","year":"2006","unstructured":"Pascale, P.D., Vasile, M.: Preliminary design of low-thrust multiple gravity-assist trajectories. J. Spacecr. Rocket. 43(5), 1065\u20131076 (2006). https:\/\/doi.org\/10.2514\/1.19646","journal-title":"J. Spacecr. Rocket."},{"issue":"11","key":"1884_CR71","doi-asserted-by":"publisher","first-page":"2485","DOI":"10.2514\/1.G001920","volume":"39","author":"E Pellegrini","year":"2016","unstructured":"Pellegrini, E., Russell, R.P.: On the computation and accuracy of trajectory state transition matrices. J. Guid. Control Dyn. 39(11), 2485\u20132499 (2016). https:\/\/doi.org\/10.2514\/1.G001920","journal-title":"J. Guid. Control Dyn."},{"key":"1884_CR72","unstructured":"Pellegrini, E., Russell, R.P.: Multiple-shooting differential dynamic programming with applications to spacecraft trajectory optimization. Ph.D. thesis (2017)"},{"issue":"11","key":"1884_CR73","doi-asserted-by":"publisher","first-page":"1603","DOI":"10.1016\/0967-0661(95)00171-P","volume":"3","author":"F Peralta","year":"1995","unstructured":"Peralta, F., Flanagan, S.: Cassini interplanetary trajectory design. Control. Eng. Pract. 3(11), 1603\u20131610 (1995). https:\/\/doi.org\/10.1016\/0967-0661(95)00171-P","journal-title":"Control. Eng. Pract."},{"key":"1884_CR74","doi-asserted-by":"publisher","unstructured":"Petropoulos, A., Longuski, J.M.: Automated design of low-thrust gravity-assist trajectories. In: AIAA, p. 4033 (2000). https:\/\/doi.org\/10.2514\/6.2000-4033","DOI":"10.2514\/6.2000-4033"},{"issue":"5","key":"1884_CR75","doi-asserted-by":"publisher","first-page":"787","DOI":"10.2514\/1.13095","volume":"41","author":"AE Petropoulos","year":"2004","unstructured":"Petropoulos, A.E., Longuski, J.M.: Shape-based algorithm for the automated design of low-thrust, gravity assist trajectories. J. Spacecr. Rocket. 41(5), 787\u2013796 (2004). https:\/\/doi.org\/10.2514\/1.13095","journal-title":"J. Spacecr. Rocket."},{"key":"1884_CR76","unstructured":"Petropoulos, A.E., Sims, J.A.: A review of some exact solutions to the planar equations of motion of a thrusting spacecraft. In: 2nd International Symposium Low Thrust Trajectories. Toulouse, France (2002)"},{"key":"1884_CR77","first-page":"204","volume":"13","author":"ET Pitkin","year":"1966","unstructured":"Pitkin, E.T.: Second transition partial derivatives via universal variables. J. Astronaut. Sci. 13, 204\u2013207 (1966)","journal-title":"J. Astronaut. Sci."},{"issue":"R1","key":"1884_CR78","first-page":"35","volume":"3","author":"E Polak","year":"1969","unstructured":"Polak, E., Ribiere, G.: Note on convergence of conjugate direction meters. ESAIM Math. Model. Numer. Anal. Math. Math. Numer. Anal. 3(R1), 35\u201343 (1969)","journal-title":"ESAIM Math. Model. Numer. Anal. Math. Math. Numer. Anal."},{"key":"1884_CR79","unstructured":"Rao, A.V.: A survey of numerical methods for optimal control. In: AAS\/AIAA Astrodynamics Specialist Conference, AAS 09\u2013334. Pittsburgh, PA (2009)"},{"issue":"10","key":"1884_CR80","doi-asserted-by":"publisher","first-page":"2250","DOI":"10.2514\/1.G000342","volume":"39","author":"J Roa","year":"2016","unstructured":"Roa, J., Pel\u00e1ez, J., Senent, J.: Spiral Lambert\u2019s problem. J. Guid. Control. Dyn. 39(10), 2250\u20132263 (2016). https:\/\/doi.org\/10.2514\/1.G000342","journal-title":"J. Guid. Control. Dyn."},{"key":"1884_CR81","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s10569-019-9927-z","volume":"131","author":"RP Russell","year":"2019","unstructured":"Russell, R.P.: On the solution to every Lambert problem. Celest. Mech. Dyn. Astron. 131, 50 (2019). https:\/\/doi.org\/10.1007\/s10569-019-9927-z","journal-title":"Celest. Mech. Dyn. Astron."},{"issue":"2","key":"1884_CR82","doi-asserted-by":"publisher","first-page":"354","DOI":"10.2514\/1.13652","volume":"29","author":"RP Russell","year":"2006","unstructured":"Russell, R.P., Ocampo, C.A.: Optimization of a broad class of ephemeris model earth\u2013mars cyclers. J. Guid. Control. Dyn. 29(2), 354\u2013367 (2006). https:\/\/doi.org\/10.2514\/1.13652","journal-title":"J. Guid. Control. Dyn."},{"issue":"6","key":"1884_CR83","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.2514\/3.21331","volume":"17","author":"WA Scheel","year":"1994","unstructured":"Scheel, W.A., Conway, B.A.: Optimization of very-low-thrust, many-revolution spacecraft trajectories. J. Guid. Control. Dyn. 17(6), 1185\u20131192 (1994). https:\/\/doi.org\/10.2514\/3.21331","journal-title":"J. Guid. Control. Dyn."},{"issue":"111","key":"1884_CR84","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1090\/S0025-5718-1970-0274029-X","volume":"24","author":"DF Shanno","year":"1970","unstructured":"Shanno, D.F.: Conditioning of quasi-newton methods for function minimization. Math. Comput. 24(111), 647\u2013656 (1970). https:\/\/doi.org\/10.1090\/S0025-5718-1970-0274029-X","journal-title":"Math. Comput."},{"key":"1884_CR85","doi-asserted-by":"publisher","unstructured":"Shannon, J.L., Ozimek, M.T., Atchison, J.A., Hartzell, C.M.: Q-law aided direct trajectory optimization of many-revolution low-thrust transfers. J. Spacecr. Rocket. (2020). https:\/\/doi.org\/10.2514\/1.A34586","DOI":"10.2514\/1.A34586"},{"issue":"2","key":"1884_CR86","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF01227666","volume":"35","author":"SW Shepperd","year":"1985","unstructured":"Shepperd, S.W.: Universal Keplerian state transition matrix. Celest. Mech. 35(2), 129\u2013144 (1985). https:\/\/doi.org\/10.1007\/BF01227666","journal-title":"Celest. Mech."},{"key":"1884_CR87","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.paerosci.2018.07.007","volume":"102","author":"A Shirazi","year":"2018","unstructured":"Shirazi, A., Ceberio, J., Lozano, J.A.: Spacecraft trajectory optimization: a review of models, objectives, approaches, and solutions. Prog. Aerosp. Sci. 102, 76\u201398 (2018). https:\/\/doi.org\/10.1016\/j.paerosci.2018.07.007","journal-title":"Prog. Aerosp. Sci."},{"key":"1884_CR88","doi-asserted-by":"publisher","unstructured":"Sims, J.A., Finlayson, P.A., Rinderle, E.A., Vavrina, M.A., Kowalkowski, T.D.: Implementation of a low-thrust trajectory optimization algorithm for preliminary design. In: AAS\/AIAA Astrodynamics Specialist Conference, AIAA 2006-6746. Keystone, Colorado (2006). https:\/\/doi.org\/10.2514\/6.2006-6746","DOI":"10.2514\/6.2006-6746"},{"key":"1884_CR89","doi-asserted-by":"crossref","unstructured":"Smith, J., Buffington, B.: Overview of the cassini solstice mission trajectory. In: AAS\/AIAA Advances in the Astronautical Sciences, AAS 2009-351, vol. 135. Pittsburgh, PA (2009)","DOI":"10.2514\/6.2008-6752"},{"key":"1884_CR90","doi-asserted-by":"publisher","unstructured":"Strange, N., Goodson, T., Hahn, Y.: Cassini tour redesign for the huygens mission. In: AIAA\/AAS Astrodynamics Specialist Conference and Exhibit, AIAA 2002-4720. Monterey, California (2002). https:\/\/doi.org\/10.2514\/6.2002-4720","DOI":"10.2514\/6.2002-4720"},{"issue":"3","key":"1884_CR91","doi-asserted-by":"publisher","first-page":"535","DOI":"10.2514\/1.58789","volume":"49","author":"E Taheri","year":"2012","unstructured":"Taheri, E., Abdelkhalik, O.: Shape-based approximation of constrained low-thrust space trajectories using Fourier series. J. Spacecr. Rocket. 49(3), 535\u2013546 (2012). https:\/\/doi.org\/10.2514\/1.58789","journal-title":"J. Spacecr. Rocket."},{"key":"1884_CR92","unstructured":"Vasile, M., Ceriotti, M., Radice, G., Becerra, V.M., Nasuto, S.J., Anderson, J.D.: Global trajectory optimisation: can we prune the solution space when considering deep space manoeuvres? (2008)"},{"issue":"1","key":"1884_CR93","doi-asserted-by":"publisher","first-page":"12","DOI":"10.2514\/3.49622","volume":"13","author":"CE Velez","year":"1975","unstructured":"Velez, C.E., Fuchs, A.J.: Averaging techniques and their application to orbit determination systems. AIAA J. 13(1), 12\u201316 (1975). https:\/\/doi.org\/10.2514\/3.49622","journal-title":"AIAA J."},{"issue":"1","key":"1884_CR94","doi-asserted-by":"publisher","first-page":"95","DOI":"10.2514\/1.36848","volume":"32","author":"BJ Wall","year":"2009","unstructured":"Wall, B.J., Conway, B.A.: Shape-based approach to low-thrust rendezvous trajectory design. J. Guid. Control Dyn. 32(1), 95\u2013101 (2009). https:\/\/doi.org\/10.2514\/1.36848","journal-title":"J. Guid. Control Dyn."},{"key":"1884_CR95","unstructured":"Whiffen, G.J.: Static\/dynamic control for optimizing a useful objective (2002). US Patent 6,496,741"},{"issue":"5","key":"1884_CR96","doi-asserted-by":"publisher","first-page":"865","DOI":"10.2514\/2.4616","volume":"23","author":"OA Yakimenko","year":"2000","unstructured":"Yakimenko, O.A.: Direct method for rapid prototyping of near-optimal aircraft trajectories. J. Guid. Control Dyn. 23(5), 865\u2013875 (2000). https:\/\/doi.org\/10.2514\/2.4616","journal-title":"J. Guid. Control Dyn."},{"key":"1884_CR97","unstructured":"Yam, C.H., Izzo, D., Biscani, F.: Towards a high fidelity direct transcription method for optimisation of low-thrust trajectories. In: 4th International Conference on Astrodynamics Tools and Techniques, pp. 1\u20137 (2010)"},{"issue":"4","key":"1884_CR98","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1016\/S1000-9361(08)60121-1","volume":"22","author":"G Yang","year":"2009","unstructured":"Yang, G.: Direct optimization of low-thrust many-revolution earth-orbit transfers. Chin. J. Aeronaut. 22(4), 426\u2013433 (2009). https:\/\/doi.org\/10.1016\/S1000-9361(08)60121-1","journal-title":"Chin. J. Aeronaut."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01884-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-021-01884-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01884-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T18:15:10Z","timestamp":1636568110000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-021-01884-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,14]]},"references-count":98,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["1884"],"URL":"https:\/\/doi.org\/10.1007\/s10957-021-01884-1","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,14]]},"assertion":[{"value":"28 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}