Higher Order Algorithm for Solving Lambert’s Problem
This work presents a high-order perturbation expansion method for solving Lambert’s problem. The necessary condition for the problem is defined by a fourth-order Taylor expansion of the terminal error vector. The Taylor expansion partial derivative models are generated by Computational Differentiati...
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| Veröffentlicht in: | The Journal of the astronautical sciences 2018-12, Vol.65 (4), p.400-422 |
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| container_title | The Journal of the astronautical sciences |
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| creator | Alhulayil, Mohammad Younes, Ahmad Bani Turner, James D. |
| description | This work presents a high-order perturbation expansion method for solving Lambert’s problem. The necessary condition for the problem is defined by a fourth-order Taylor expansion of the terminal error vector. The Taylor expansion partial derivative models are generated by Computational Differentiation (CD) tools. A novel derivative enhanced numerical integration algorithm is presented for computing nonlinear state transition tensors, where only the equation of motion is coded. A high-order successive approximation algorithm is presented for inverting the problems nonlinear necessary condition. Closed-form expressions are obtained for the first, second,third, and fourth order perturbation expansion coefficients. Numerical results are presented that compare the convergence rate and accuracy of first-through fourth-order expansions. The initial p-iteration starting guess is used as the Lambert’s algorithm initial condition. Numerical experiments demonstrate that accelerated convergence is achieved for the second-, third-, and fourth-order expansions, when compared to a classical first-order Newton method. |
| doi_str_mv | 10.1007/s40295-018-0137-9 |
| format | Article |
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Numerical experiments demonstrate that accelerated convergence is achieved for the second-, third-, and fourth-order expansions, when compared to a classical first-order Newton method.</description><subject>Aerospace Technology and Astronautics</subject><subject>Algorithms</subject><subject>Convergence</subject><subject>Engineering</subject><subject>Equations of motion</subject><subject>Iterative methods</subject><subject>Mathematical Applications in the Physical Sciences</subject><subject>Mathematical models</subject><subject>Newton methods</subject><subject>Numerical integration</subject><subject>Perturbation methods</subject><subject>Software</subject><subject>Space Exploration and Astronautics</subject><subject>Space Sciences (including Extraterrestrial Physics</subject><subject>Taylor series</subject><subject>Tensors</subject><subject>Thermal expansion</subject><issn>0021-9142</issn><issn>2195-0571</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1Kw0AQxxdRsFYfwFvAc3Rnd7Mfx1LUCoUK6nnZJJM0JWnqbip48zV8vT6JWyJ48jAzMPw_4EfINdBboFTdBUGZyVIKOg5XqTkhEwbHT6bglEwoZZAaEOycXISwoZQDNTAhctHUa_TJypdxz9q6982w7pKq98lL33402zpZui5HPxy-vkPy7Pu8xe6SnFWuDXj1e6fk7eH-db5Il6vHp_lsmRYc5JACLwV1xjEsgUsp0WUUQApd6gxzkefOcIW6UBqFxJxDpQtZGCUkLSt0mk_JzZi78_37HsNgN_3eb2OlZcCNzBiAiioYVYXvQ_BY2Z1vOuc_LVB7xGNHPDbisUc81kQPGz0harc1-r_k_00_QCZnVw</recordid><startdate>20181215</startdate><enddate>20181215</enddate><creator>Alhulayil, Mohammad</creator><creator>Younes, Ahmad Bani</creator><creator>Turner, James D.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-8415-7264</orcidid></search><sort><creationdate>20181215</creationdate><title>Higher Order Algorithm for Solving Lambert’s Problem</title><author>Alhulayil, Mohammad ; Younes, Ahmad Bani ; Turner, James D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-13d40a9a2ed13666ea5011648d85eb4bba937e8c78e46eb31f8c6c97460dfea83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Aerospace Technology and Astronautics</topic><topic>Algorithms</topic><topic>Convergence</topic><topic>Engineering</topic><topic>Equations of motion</topic><topic>Iterative methods</topic><topic>Mathematical Applications in the Physical Sciences</topic><topic>Mathematical models</topic><topic>Newton methods</topic><topic>Numerical integration</topic><topic>Perturbation methods</topic><topic>Software</topic><topic>Space Exploration and Astronautics</topic><topic>Space Sciences (including Extraterrestrial Physics</topic><topic>Taylor series</topic><topic>Tensors</topic><topic>Thermal expansion</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alhulayil, Mohammad</creatorcontrib><creatorcontrib>Younes, Ahmad Bani</creatorcontrib><creatorcontrib>Turner, James D.</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of the astronautical sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alhulayil, Mohammad</au><au>Younes, Ahmad Bani</au><au>Turner, James D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Higher Order Algorithm for Solving Lambert’s Problem</atitle><jtitle>The Journal of the astronautical sciences</jtitle><stitle>J of Astronaut Sci</stitle><date>2018-12-15</date><risdate>2018</risdate><volume>65</volume><issue>4</issue><spage>400</spage><epage>422</epage><pages>400-422</pages><issn>0021-9142</issn><eissn>2195-0571</eissn><abstract>This work presents a high-order perturbation expansion method for solving Lambert’s problem. The necessary condition for the problem is defined by a fourth-order Taylor expansion of the terminal error vector. The Taylor expansion partial derivative models are generated by Computational Differentiation (CD) tools. A novel derivative enhanced numerical integration algorithm is presented for computing nonlinear state transition tensors, where only the equation of motion is coded. A high-order successive approximation algorithm is presented for inverting the problems nonlinear necessary condition. Closed-form expressions are obtained for the first, second,third, and fourth order perturbation expansion coefficients. Numerical results are presented that compare the convergence rate and accuracy of first-through fourth-order expansions. The initial p-iteration starting guess is used as the Lambert’s algorithm initial condition. 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| subjects | Aerospace Technology and Astronautics Algorithms Convergence Engineering Equations of motion Iterative methods Mathematical Applications in the Physical Sciences Mathematical models Newton methods Numerical integration Perturbation methods Software Space Exploration and Astronautics Space Sciences (including Extraterrestrial Physics Taylor series Tensors Thermal expansion |
| title | Higher Order Algorithm for Solving Lambert’s Problem |
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