Adiabatic invariants drive rhythmic human motion in variable gravity

Creeping granular motion under variable gravity levels.

In a rotating tumbler that is more than one-half filled with a granular material, a core of material forms that should ideally rotate with the tumbler. However, the core rotates slightly faster than the tumbler (precession) and decreases in size (erosion). The precession and erosion of the core provide a measure of the creeping granular motion that occurs beneath a continuously flowing flat sur...

Notes on Adiabatic Invariants

Theory of Adiabatic Invariants

We review the basic theory on adiabatic invariants in classical and quantum mechanics. PACS numbers: 45.30.+s,05.45.-a,03.65.-w, 03.65.Sq

Preservation of Adiabatic Invariants under

Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example , in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to small uctuations that scale with the order of the method. In this paper, we discuss a qualitative fea...

Adiabatic Invariants and Mixmaster Catastrophes

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the ch...