Small oscillations of the pendulum, Euler's method, and adequality
  Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well-posedness based on a relation of adequality following Fermat and Leibniz. The result is that the period of infinitesimal oscillations is independent of their amplitude.   Keywords: harmonic motion; infinitesimal; pendulum; small oscillations 
Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Tahl Nowik
math.HO math-ph math.LO math.MP