Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable

Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect...
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Autor*in:	Ivanyukhin, Alexey [verfasserIn] Petukhov, Viacheslav [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Limited power trajectory Trajectory optimization Maximum principle Continuation method

Anmerkung:	© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

Übergeordnetes Werk:	Enthalten in: Journal of optimization theory and applications - Dordrecht [u.a.] : Springer Science + Business Media, 1967, 191(2021), 2-3 vom: 28. Apr., Seite 575-599
Übergeordnetes Werk:	volume:191 ; year:2021 ; number:2-3 ; day:28 ; month:04 ; pages:575-599

Links:	Volltext

DOI / URN:	10.1007/s10957-021-01853-8

Katalog-ID:	SPR045529507

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520			\|a Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity.
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allfields	10.1007/s10957-021-01853-8 doi (DE-627)SPR045529507 (SPR)s10957-021-01853-8-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Ivanyukhin, Alexey verfasserin aut Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. Limited power trajectory (dpeaa)DE-He213 Trajectory optimization (dpeaa)DE-He213 Maximum principle (dpeaa)DE-He213 Continuation method (dpeaa)DE-He213 Petukhov, Viacheslav verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 191(2021), 2-3 vom: 28. Apr., Seite 575-599 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599 https://dx.doi.org/10.1007/s10957-021-01853-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 191 2021 2-3 28 04 575-599
spelling	10.1007/s10957-021-01853-8 doi (DE-627)SPR045529507 (SPR)s10957-021-01853-8-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Ivanyukhin, Alexey verfasserin aut Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. Limited power trajectory (dpeaa)DE-He213 Trajectory optimization (dpeaa)DE-He213 Maximum principle (dpeaa)DE-He213 Continuation method (dpeaa)DE-He213 Petukhov, Viacheslav verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 191(2021), 2-3 vom: 28. Apr., Seite 575-599 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599 https://dx.doi.org/10.1007/s10957-021-01853-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 191 2021 2-3 28 04 575-599
allfields_unstemmed	10.1007/s10957-021-01853-8 doi (DE-627)SPR045529507 (SPR)s10957-021-01853-8-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Ivanyukhin, Alexey verfasserin aut Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. Limited power trajectory (dpeaa)DE-He213 Trajectory optimization (dpeaa)DE-He213 Maximum principle (dpeaa)DE-He213 Continuation method (dpeaa)DE-He213 Petukhov, Viacheslav verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 191(2021), 2-3 vom: 28. Apr., Seite 575-599 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599 https://dx.doi.org/10.1007/s10957-021-01853-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 191 2021 2-3 28 04 575-599
allfieldsGer	10.1007/s10957-021-01853-8 doi (DE-627)SPR045529507 (SPR)s10957-021-01853-8-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Ivanyukhin, Alexey verfasserin aut Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. Limited power trajectory (dpeaa)DE-He213 Trajectory optimization (dpeaa)DE-He213 Maximum principle (dpeaa)DE-He213 Continuation method (dpeaa)DE-He213 Petukhov, Viacheslav verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 191(2021), 2-3 vom: 28. Apr., Seite 575-599 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599 https://dx.doi.org/10.1007/s10957-021-01853-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 191 2021 2-3 28 04 575-599
allfieldsSound	10.1007/s10957-021-01853-8 doi (DE-627)SPR045529507 (SPR)s10957-021-01853-8-e DE-627 ger DE-627 rakwb eng 330 510 000 ASE 31.80 bkl Ivanyukhin, Alexey verfasserin aut Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. Limited power trajectory (dpeaa)DE-He213 Trajectory optimization (dpeaa)DE-He213 Maximum principle (dpeaa)DE-He213 Continuation method (dpeaa)DE-He213 Petukhov, Viacheslav verfasserin aut Enthalten in Journal of optimization theory and applications Dordrecht [u.a.] : Springer Science + Business Media, 1967 191(2021), 2-3 vom: 28. Apr., Seite 575-599 (DE-627)266883923 (DE-600)1468244-8 1573-2878 nnns volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599 https://dx.doi.org/10.1007/s10957-021-01853-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_26 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.80 ASE AR 191 2021 2-3 28 04 575-599
language	English
source	Enthalten in Journal of optimization theory and applications 191(2021), 2-3 vom: 28. Apr., Seite 575-599 volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599
sourceStr	Enthalten in Journal of optimization theory and applications 191(2021), 2-3 vom: 28. Apr., Seite 575-599 volume:191 year:2021 number:2-3 day:28 month:04 pages:575-599
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Limited power trajectory Trajectory optimization Maximum principle Continuation method
dewey-raw	330
isfreeaccess_bool	false
container_title	Journal of optimization theory and applications
authorswithroles_txt_mv	Ivanyukhin, Alexey @@aut@@ Petukhov, Viacheslav @@aut@@
publishDateDaySort_date	2021-04-28T00:00:00Z
hierarchy_top_id	266883923
dewey-sort	3330
id	SPR045529507
language_de	englisch
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author	Ivanyukhin, Alexey
spellingShingle	Ivanyukhin, Alexey ddc 330 bkl 31.80 misc Limited power trajectory misc Trajectory optimization misc Maximum principle misc Continuation method Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable
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topic_title	330 510 000 ASE 31.80 bkl Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable Limited power trajectory (dpeaa)DE-He213 Trajectory optimization (dpeaa)DE-He213 Maximum principle (dpeaa)DE-He213 Continuation method (dpeaa)DE-He213
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title	Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable
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title_full	Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable
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title_sort	optimization of multi-revolution limited power trajectories using angular independent variable
title_auth	Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable
abstract	Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
abstractGer	Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
abstract_unstemmed	Abstract Optimization of low-thrust trajectories is necessary in the design of space missions using electric propulsion systems. We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. The high computational performance of the developed technique makes it possible to carry out and present an analysis of the angular flight range and initial true longitude impact on the cost function, transfer duration, and characteristic velocity. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021
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title_short	Optimization of Multi-revolution Limited Power Trajectories Using Angular Independent Variable
url	https://dx.doi.org/10.1007/s10957-021-01853-8
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author2	Petukhov, Viacheslav
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up_date	2024-07-03T16:36:16.322Z
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We consider the problem of limited power trajectory optimization, which is a well-known case of the low-thrust optimization problem. In the article, we present an indirect approach to trajectory optimization based on the use of the maximum principle and the continuation method. We introduce the concept of auxiliary longitude and use it as a new independent variable instead of time. The use of equations of motion in the equinoctial elements and a new independent variable allowed us to simplify the optimization of limited power trajectories with a fixed angular distance and free transfer duration. The article presents a new form of necessary optimality conditions for this problem and describes an efficient new numerical method to solve the limited power trajectory optimization problem. We show the existence of several trajectories with a fixed transfer duration and free angular distance that satisfy the necessary optimality conditions. Using numerical examples, we confirm the existence of the limiting values of the characteristic velocity and the product of the cost function value and the transfer duration as the angular distance increases. 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