{"title":"天体力学中的扰动理论和典型坐标","authors":"Gabriella Pinzari","doi":"10.1142/s0129055x24300061","DOIUrl":null,"url":null,"abstract":"<p>KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.</p>","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"77 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Perturbation theory and canonical coordinates in celestial mechanics\",\"authors\":\"Gabriella Pinzari\",\"doi\":\"10.1142/s0129055x24300061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.</p>\",\"PeriodicalId\":54483,\"journal\":{\"name\":\"Reviews in Mathematical Physics\",\"volume\":\"77 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-04-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reviews in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1142/s0129055x24300061\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reviews in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s0129055x24300061","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
KAM 理论的成功主要归功于其最初的动机:应用于天体力学问题。60 年代,阿诺德提出了一个专门用于行星问题的定理,并将其命名为 "基本定理"(FT)。然而,只有在大约 50 年后,一套建设性地考虑到旋转不变性和近似可动性的坐标被使用时,FT 才能真正用于这一目的。从那时起,对该问题的交映评估取得了一些进展,在此我们对这些成果进行回顾。
Perturbation theory and canonical coordinates in celestial mechanics
KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.
期刊介绍:
Reviews in Mathematical Physics fills the need for a review journal in the field, but also accepts original research papers of high quality. The review papers - introductory and survey papers - are of relevance not only to mathematical physicists, but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Original research papers are not subject to page limitations provided they are of importance to this readership. It is desirable that such papers have an expository part understandable to a wider readership than experts. Papers with the character of a scientific letter are usually not suitable for RMP.