{"title":"有限时间范围两点边值问题的最小作用原理及解","authors":"W. McEneaney, P. Dower","doi":"10.1137/1.9781611973273.27","DOIUrl":null,"url":null,"abstract":"Two-point boundary problems for conservative systems are studied in the context of the least action principle. The emphasis is on the N -body problem under gravitation. There, the least action principle optimal control problem is converted to a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. For problems where the time-duration is below a specified bound, fundamental solutions are obtained as indexed sets of solutions of Riccati equations.","PeriodicalId":193106,"journal":{"name":"SIAM Conf. on Control and its Applications","volume":"48 9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":"{\"title\":\"The Principle of Least Action and Solution of Two-Point Boundary Value Problems on a Limited Time Horizon\",\"authors\":\"W. McEneaney, P. Dower\",\"doi\":\"10.1137/1.9781611973273.27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two-point boundary problems for conservative systems are studied in the context of the least action principle. The emphasis is on the N -body problem under gravitation. There, the least action principle optimal control problem is converted to a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. For problems where the time-duration is below a specified bound, fundamental solutions are obtained as indexed sets of solutions of Riccati equations.\",\"PeriodicalId\":193106,\"journal\":{\"name\":\"SIAM Conf. on Control and its Applications\",\"volume\":\"48 9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"18\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Conf. on Control and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9781611973273.27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Conf. on Control and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611973273.27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Principle of Least Action and Solution of Two-Point Boundary Value Problems on a Limited Time Horizon
Two-point boundary problems for conservative systems are studied in the context of the least action principle. The emphasis is on the N -body problem under gravitation. There, the least action principle optimal control problem is converted to a differential game, where an opposing player maximizes over an indexed set of quadratics to yield the gravitational potential. For problems where the time-duration is below a specified bound, fundamental solutions are obtained as indexed sets of solutions of Riccati equations.
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