Numerical evidence for the approximation of dissipative systems by gyroscopically coupled oscillator chains
Alberto Maria Bersani, Paolo Caressa, Alessandro Ciallella
Abstract
Inspired by the equations of motion of the gyroscope, where a Lagrangian and conservative system may appear to mimic a dissipative one when focusing on a single degree of freedom for finite time intervals, we introduce a gyroscopic-type coupling between harmonic oscillators. The aim is to propose a tentative scheme of solution for the problem of finding a higher-dimensional Lagrangian system approximating a lower-dimensional dissipative one. Specifically, we consider a certain family of Lagrangian systems, for which the time evolution of the first Lagrangian parameter is conjectured to be a good approximation for the evolution of a one-dimensional linear dissipative system in finite time intervals, up to a fixed precision. The behavior of the selected family of gyroscopic couplings is compared with a given dissipative system, properly optimizing a family of parameters according to a described scheme. Numerical calculations are reported, suggesting the validity of the proposed conjecture.