{"title":"规范的转换","authors":"G. Kotkin, V. Serbo","doi":"10.1093/oso/9780198853787.003.0011","DOIUrl":null,"url":null,"abstract":"This chapter addresses the canonical transformation defined by the given generating function, the rotation in the phase space as a canonical transformation, and themovement of the system as a canonical transformation. The chapter also discusses using the canonical transformations for solving the problems of the anharmonic oscillations and using the canonical transformation to diagonalize the Hamiltonian function of an anisotropic charged harmonic oscillator in a magnetic field. Finally, the chapter addresses the canonical variables which reduce the Hamiltonian function of the harmonic oscillator to zero and using them for consideration of the system of the harmonic oscillators with the weak nonlinear coupling.","PeriodicalId":201389,"journal":{"name":"Exploring Classical Mechanics","volume":"559 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Canonical transformations\",\"authors\":\"G. Kotkin, V. Serbo\",\"doi\":\"10.1093/oso/9780198853787.003.0011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This chapter addresses the canonical transformation defined by the given generating function, the rotation in the phase space as a canonical transformation, and themovement of the system as a canonical transformation. The chapter also discusses using the canonical transformations for solving the problems of the anharmonic oscillations and using the canonical transformation to diagonalize the Hamiltonian function of an anisotropic charged harmonic oscillator in a magnetic field. Finally, the chapter addresses the canonical variables which reduce the Hamiltonian function of the harmonic oscillator to zero and using them for consideration of the system of the harmonic oscillators with the weak nonlinear coupling.\",\"PeriodicalId\":201389,\"journal\":{\"name\":\"Exploring Classical Mechanics\",\"volume\":\"559 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Exploring Classical Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/oso/9780198853787.003.0011\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Exploring Classical Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780198853787.003.0011","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This chapter addresses the canonical transformation defined by the given generating function, the rotation in the phase space as a canonical transformation, and themovement of the system as a canonical transformation. The chapter also discusses using the canonical transformations for solving the problems of the anharmonic oscillations and using the canonical transformation to diagonalize the Hamiltonian function of an anisotropic charged harmonic oscillator in a magnetic field. Finally, the chapter addresses the canonical variables which reduce the Hamiltonian function of the harmonic oscillator to zero and using them for consideration of the system of the harmonic oscillators with the weak nonlinear coupling.
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