Variations on the adiabatic invariance: the Lorentz pendulum
  We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in both pendula and put in evidence their substantially different physical behavior with regard to adiabatic invariance. 
Luis L.Sanchez-Soto and J. Zoido
physics.class-ph math-ph math.MP quant-ph