The Milgrom oscillator

Abstract

The Milgrom oscillator is an oscillator working in the Modified Newtonian Dynamics (MOND) setting. A brief description of MOND is given. The equation of a Milgrom oscillator is deduced. An analogy with a classical system is built and in its setting both the kinetic and potential energies are computed. The law of conservation of energy is recovered. Different regimes of the oscillator are presented. Next, its periodic character is studied through numerical simulations. A discussion of the difficulties of testing MOND with the Milgrom oscillator ends the paper.