2016/12/13 by A. Bocci, Bocci, Alessio, Giovanni Mingari Scarpello +3
Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Experimental and Theoretical Physics Studies #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1612.04253
openalex publication_date 2016/12/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We model the dynamical behavior of a three dimensional (3-D) dissipative\noscillator consisting of a m-block whose vertical fall occurs against a\nspring and which can also slide horizontally on a rigid truss rotating at a\nknown angular speed law \ω(t). The z-vertical time law is obvious,\nwhilst its x-motion along the horizontal arm is ruled by a linear\ndifferential equation to be solved through the Hermite functions and the\nConfluent Hypergeometric Function (CHF) 1F1 (Kummer). After the\nrotation time law \θ(t) has been computed, we know completely the mass\nmotion in a cylindrical coordinate reference: some transients have then been\ndiscussed. Finally, further effects as an inclined slide and a contact dry\nfriction have been added to the problem, so that the motion differential\nequation becomes inhomogeneous and we resort to Lagrange method of variation of\nconstants, helped by a Fourier-Bessel expansion, in order to manage the\nrelevant intractable integrations.\n