Classical harmonic three-body system: An experimental electronic realization

Abstract

The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point masses $(m_1,m_2,m_3)$ with arbitrary pairwise potential $V(r_{ij})$ that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the system parameters and initial conditions are independently controlled via voltage signals. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment.