2017/03/31 by Przemysław Brzykcy, Przemyslaw Brzykcy
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Dissipative system #Harmonic oscillator #Homotopy and Cohomology in Algebraic Topology #Lie algebra #Lie group #Nonlinear Waves and Solitons #Orbit (dynamics) #Phase space #Realisation #Simple (philosophy) #Simple harmonic motion #math-ph #math.MP
paper · pdf · doi:10.1063/1.4986383
10 pages, 1 figure
arxiv created 2017/05/16 · openalex publication_date 2018/03/01 · openalex created_date 2018/03/29 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillator is indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the orbit method. An in-depth analysis of the coadjoint orbits of the (1 + 1) dimensional Newton-Hooke group is presented. Furthermore, it is argued that the physical interpretation is carried by a specific realisation of the Lie algebra of smooth functions on a phase space rather than by an abstract Lie algebra.