Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling

摘要: We explore the relation between classical continuum model of Euler buckling and an iterated mapping which is not only a mathematical discretization former but also has exact, discrete mechanical analogue. show that latter possesses great numbers “parasitic” solutions in addition to natural discretizations modes. investigate this rich bifurcational structure using both analysis boundary value problem dynamical studies initial problem, familiar standard map. use example links problems and, more generally, illustrate complex relations among physical systems, models analytical numerical methods for their study.