{"title":"非光滑机械系统仿真与控制的逆向误差分析方法","authors":"David Pekarek, T. Murphey","doi":"10.1109/CDC.2011.6160975","DOIUrl":null,"url":null,"abstract":"This paper presents an original structured integration scheme for Lagrangian systems undergoing elastic impacts due to unilateral constraints. In deriving the method, a backwards error analysis approach establishes a discrete time conservation law for impacts using the notion of a modified system Hamiltonian. Shortcomings of existing simulation methods that do not use this conservation law are demonstrated both analytically and in simulation. Relative to these methods, our scheme provides advantages in terms of discrete time energy behavior, accuracy of trajectories, and consistent order of accuracy of the method.","PeriodicalId":360068,"journal":{"name":"IEEE Conference on Decision and Control and European Control Conference","volume":"60 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"A backwards error analysis approach for simulation and control of nonsmooth mechanical systems\",\"authors\":\"David Pekarek, T. Murphey\",\"doi\":\"10.1109/CDC.2011.6160975\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents an original structured integration scheme for Lagrangian systems undergoing elastic impacts due to unilateral constraints. In deriving the method, a backwards error analysis approach establishes a discrete time conservation law for impacts using the notion of a modified system Hamiltonian. Shortcomings of existing simulation methods that do not use this conservation law are demonstrated both analytically and in simulation. Relative to these methods, our scheme provides advantages in terms of discrete time energy behavior, accuracy of trajectories, and consistent order of accuracy of the method.\",\"PeriodicalId\":360068,\"journal\":{\"name\":\"IEEE Conference on Decision and Control and European Control Conference\",\"volume\":\"60 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Conference on Decision and Control and European Control Conference\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2011.6160975\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Conference on Decision and Control and European Control Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2011.6160975","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A backwards error analysis approach for simulation and control of nonsmooth mechanical systems
This paper presents an original structured integration scheme for Lagrangian systems undergoing elastic impacts due to unilateral constraints. In deriving the method, a backwards error analysis approach establishes a discrete time conservation law for impacts using the notion of a modified system Hamiltonian. Shortcomings of existing simulation methods that do not use this conservation law are demonstrated both analytically and in simulation. Relative to these methods, our scheme provides advantages in terms of discrete time energy behavior, accuracy of trajectories, and consistent order of accuracy of the method.