The theory of elastic pseudo-rigid bodies was developed independently by Cohen [1] and Muncaster [2]. Their derivations of the theory are quite different, and, indeed, complementary. Cohen's derivation develops an exact mechanical theory for a class of objects called pseudo-rigid bodies. Muncaster, on the other hand, derives the theory as a coarse theory which, in a precise sense, approximates the theory of elasticity.The governing equations of the theory are mi~G =f, (1.1) and i~EF ~ = M e -~2.(1.2)The basic unknowns in the theory are the vector rG, the location in space of the center of mass G of the pseudo-rigid body, and the second-order tensor F which characterizes the state of deformation of the body. The quantities f, M e, are, respectively, the resultant external force and force-moment tensor with respect to G. The tensors E and 1~ are, respectively, the Euler tensor and the internal force-moment tensor of the body with respect to G. In subsequent papers [3,4], Cohen and Muncaster have applied the theory to the solution of some basic problems. In a forthcoming book [5] they set forth a unified exposition of the foundations of the theory, and present the solution to these and other problems.The present work represents a contribution to the program, initiated in [3,4], of the developing exact solutions to specific problems. Here we focus on plane motions of pseudo-rigid bodies. We especially emphasize situations where, by virtue of some combination of first integrals, symmetry, and kinematical constraints, the problem is reducible to one which can be treated by phase-plane analysis.
