{"title":"圆锥运动径向距离的通用符号表达式","authors":"M. Sharaf, A. S. Saad, A. Alshaery","doi":"10.2298/SAJ1489087S","DOIUrl":null,"url":null,"abstract":"SUMMARY: In the present paper, a universal symbolic expression for radial distance of conic motion in recursive power series form is developed. The importance of this analytical power series representation is that it is invariant under many operations because the result of addition, multiplication, exponentiation, integration, differentiation, etc. of a power series is also a power series. This is the fact that provides excellent flexibility in dealing with analytical, as well as computational developments of problems related to radial distance. For computational developments, a full recursive algorithm is developed for the series coefficients. An efficient method using the continued fraction theory is provided for series evolution, and two devices are proposed to secure the convergence when the time interval (t − t0) is large. In addition, the algorithm does not need the solution of Kepler’s equation and its variants for parabolic and hyperbolic orbits. Numerical applications of the algorithm are given for three orbits of different eccentricities; the results showed that it is accurate for any conic motion.","PeriodicalId":48878,"journal":{"name":"Serbian Astronomical Journal","volume":"189 1","pages":"87-92"},"PeriodicalIF":0.8000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Universal symbolic expression for radial distance of conic motion\",\"authors\":\"M. Sharaf, A. S. Saad, A. Alshaery\",\"doi\":\"10.2298/SAJ1489087S\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SUMMARY: In the present paper, a universal symbolic expression for radial distance of conic motion in recursive power series form is developed. The importance of this analytical power series representation is that it is invariant under many operations because the result of addition, multiplication, exponentiation, integration, differentiation, etc. of a power series is also a power series. This is the fact that provides excellent flexibility in dealing with analytical, as well as computational developments of problems related to radial distance. For computational developments, a full recursive algorithm is developed for the series coefficients. An efficient method using the continued fraction theory is provided for series evolution, and two devices are proposed to secure the convergence when the time interval (t − t0) is large. In addition, the algorithm does not need the solution of Kepler’s equation and its variants for parabolic and hyperbolic orbits. Numerical applications of the algorithm are given for three orbits of different eccentricities; the results showed that it is accurate for any conic motion.\",\"PeriodicalId\":48878,\"journal\":{\"name\":\"Serbian Astronomical Journal\",\"volume\":\"189 1\",\"pages\":\"87-92\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2014-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Serbian Astronomical Journal\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.2298/SAJ1489087S\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Serbian Astronomical Journal","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.2298/SAJ1489087S","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
Universal symbolic expression for radial distance of conic motion
SUMMARY: In the present paper, a universal symbolic expression for radial distance of conic motion in recursive power series form is developed. The importance of this analytical power series representation is that it is invariant under many operations because the result of addition, multiplication, exponentiation, integration, differentiation, etc. of a power series is also a power series. This is the fact that provides excellent flexibility in dealing with analytical, as well as computational developments of problems related to radial distance. For computational developments, a full recursive algorithm is developed for the series coefficients. An efficient method using the continued fraction theory is provided for series evolution, and two devices are proposed to secure the convergence when the time interval (t − t0) is large. In addition, the algorithm does not need the solution of Kepler’s equation and its variants for parabolic and hyperbolic orbits. Numerical applications of the algorithm are given for three orbits of different eccentricities; the results showed that it is accurate for any conic motion.
期刊介绍:
Serbian Astronomical Journal publishes original observations and researches in all branches of astronomy. The journal publishes:
Invited Reviews - review article on some up-to-date topic in astronomy, astrophysics and related fields (written upon invitation only),
Original Scientific Papers - article in which are presented previously unpublished author''s own scientific results,
Preliminary Reports - original scientific paper, but shorter in length and of preliminary nature,
Professional Papers - articles offering experience useful for the improvement of professional practice i.e. article describing methods and techniques, software, presenting observational data, etc.
In some cases the journal may publish other contributions, such as In Memoriam notes, Obituaries, Book Reviews, as well as Editorials, Addenda, Errata, Corrigenda, Retraction notes, etc.