The generalized pendulum analogy of the X-ray dynamical diffraction by one-dimensional regularly deformed crystals

The pendulum analogy has been generalized in a form suitable for the case of an off-Bragg position. It is shown that, by introducing a time variation of the pendula masses, this analogy can be supplied to simulate the X-ray dynamical diffraction by a one-dimensional regularly deformed crystal. The correspondence between the adiabatic invariants of the new mechanical system and the invariants of the Eikonal approximation of the X-ray dynamical theory is established