{"title":"Oscillations of linear chains","authors":"G. Kotkin, V. Serbo","doi":"10.1093/oso/9780198853787.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780198853787.003.0007","url":null,"abstract":"This chapter addresses chain of particles connected by springs as the simplest models used in theory of solids, the travelling and standing waves on a chain, and the free and forced oscillations of N particles which are connected by springs and which can move either along a straight line or along a ring. The chapter also addresses the free and forced oscillations of 2N particles, alternating either with masses or with elastic constants; the free and forced oscillations of the artificial line with inductances and capacitors; and the elastic rod as the limiting case of the system of N particles connected by spring in the limit N tends to infinity.","PeriodicalId":201389,"journal":{"name":"Exploring Classical Mechanics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130396514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lagrangian equations of motion. Conservation laws","authors":"G. Kotkin, V. Serbo","doi":"10.1093/oso/9780198853787.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198853787.003.0004","url":null,"abstract":"This chapter addresses the invariance of the Lagrangian equations of motion under the coordinate to transformation, the transformation of the energy and generalised momenta under the coordinate transformation. The integrals of motion for a particle moving in the field with a given symmetry to the Noether’s theorem, the Lagrangian functions, and the Lagrangian equations of motion for the electromechanical system. The authors also discuss the influence of constraints and friction on the motion of a system, the virial theorem and its generalization in the presents of a magnetic field, and an additional integral of motion for a system of three interacting particles.","PeriodicalId":201389,"journal":{"name":"Exploring Classical Mechanics","volume":"162 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132858560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}