Dynamics of a flexible beam and a system of rigid rods, with fully inverse (one-sided) boundary conditions

The problem of the fully inverse time-dependent boundary value of a flexible beam, where all six boundary conditions on one side of the beam are known, is discussed. A linear problem of a Euler beam and a nonlinear problem of a system of rigid rods with connecting rotational springs are solved analytically, and restrictions associated with the transfer of boundary conditions from one side of the beam to the other are analyzed. It is shown that if the boundary conditions are analytic, then both linear and the nonlinear solutions exist and they depend solely on these boundary constraints. A case study shows that a limited number of rod elements and time derivatives of the boundary conditions is sufficient in such cases for close simulation of a flexible beam. Possible applications of the fully inverse solution in the areas of robotics and measurement are discussed.