{"title":"斯塔克哈密顿量的归一化与约化","authors":"R. Cushman","doi":"10.3934/cam.2023022","DOIUrl":null,"url":null,"abstract":"We detail a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo-Stiefel mapping. After reduction, we obtain an integrable two degree of freedom system on $ S^2_h \\times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.","PeriodicalId":233941,"journal":{"name":"Communications in Analysis and Mechanics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Normalization and reduction of the Stark Hamiltonian\",\"authors\":\"R. Cushman\",\"doi\":\"10.3934/cam.2023022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We detail a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo-Stiefel mapping. After reduction, we obtain an integrable two degree of freedom system on $ S^2_h \\\\times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.\",\"PeriodicalId\":233941,\"journal\":{\"name\":\"Communications in Analysis and Mechanics\",\"volume\":\"48 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Analysis and Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/cam.2023022\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/cam.2023022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Normalization and reduction of the Stark Hamiltonian
We detail a calculation of the second order normal form of the Stark effect Hamiltonian after regularization, using the Kustaanheimo-Stiefel mapping. After reduction, we obtain an integrable two degree of freedom system on $ S^2_h \times S^2_h $, which we reduce again to obtain a one degree of freedom Hamiltonian system.
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