Abstract: For the simple Rigid Flexible Coupling system with a central rigid body and a mounted cantilever beam, the mathematical models of Euler Bernoulli beam in earlier papers have serious defect. In the present work, a nonlinear mathematical model of the system with a finite deforming beam on the assumption that its constitutive relation in linearly elastic, using the Differential Element Method and Variational Method, is obtained. In using strict method to analyse this nonlinearly coupling dynamic system, we u...