Plane motions of elastic pseudo-rigid pendulums

The basic equations are stated for pseudo-rigid bodies in their referential form for the special cases in which the base point either is a fixed point of the motion or else is moving with the center of mass. This is followed by a discussion of first integrals, conservation of energy and constitutive theory. We address the problem of the elastic planar pendulum and write the equations of motion in terms of a swing angle and the three components of the two-dimensional stretch tensor. An analysis of the static equilibrium positions of the pendulum is presented. The last two sections deal with oscillatory solutions for semi-linear elastic pendulums. The phenomenon of nonlinear resonance is identified and treated for bodies with and without internal constraints and the results of a numerical analysis are presented in detailed graphical form.