• Login
    View Item 
    •   ResearchSpace Home
    • College of Agriculture, Engineering and Science
    • School Mathematics, Statistics and Computer Science
    • Pure Mathematics
    • Masters Degrees (Pure Mathematics)
    • View Item
    •   ResearchSpace Home
    • College of Agriculture, Engineering and Science
    • School Mathematics, Statistics and Computer Science
    • Pure Mathematics
    • Masters Degrees (Pure Mathematics)
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Ermakov systems : a group theoretic approach.

    Thumbnail
    View/Open
    Govinder_K_S_1993.pdf (3.355Mb)
    Date
    1993
    Author
    Govinder, Keshlan Sathasiva.
    Metadata
    Show full item record
    Abstract
    The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) are two examples that jointly and separately describe many physical situations. We study Ermakov systems from the point of view of the algebraic properties of differential equations. The idea of generalised Ermakov systems is introduced and their relationship to the Lie algebra sl(2, R) is explained. We show that the 'compact' form of generalized Ermakov systems has an infinite dimensional Lie algebra. Such algebras are usually associated only with first order equations in the context of ordinary differential equations. Apart from the Ermakov invariant which shares the infinite-dimensional algebra of the 'compact' equation, the other three integrals force the dimension of the algebra to be reduced to the three of sl(2, R). Subsequently we establish a new class of Ermakov systems by considering equations invariant under sl(2, R) (in two dimensions) and sl(2, R) EB so(3) (in three dimensions). The former class contains the generalized Ermakov system as a special case in which the force is velocity-independent. The latter case is a generalization of the classical equation of motion of the magnetic monopole which is well known to possess the conserved Poincare vector. We demonstrate that in fact there are three such vectors for all equations of this type.
    URI
    http://hdl.handle.net/10413/5951
    Collections
    • Masters Degrees (Pure Mathematics) [27]

    DSpace software copyright © 2002-2013  Duraspace
    Contact Us | Send Feedback
    Theme by 
    @mire NV
     

     

    Browse

    All of ResearchSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsAdvisorsTypeThis CollectionBy Issue DateAuthorsTitlesSubjectsAdvisorsType

    My Account

    LoginRegister

    DSpace software copyright © 2002-2013  Duraspace
    Contact Us | Send Feedback
    Theme by 
    @mire NV