Equations of motion for a deformable cylinder moving in an inviscid fluid

The paper tries to derive equations of motion for a symmetric body with unevenly-distributed density deforming symmetrically in an inviscid fluid to explain self-propelled motion of a deformable body through fluids. Our focus is only on a simple two-dimensional body with large deformation. As a result, the velocity potential of an equi-curvature bending plate moving through the otherwise quiescent fluid is obtained. The plate density is assumed to be linearly changeable along its longitudinal sense. From the formulae given by Sedov, the equations of motion for the bending plate are acquired. Then, some important conclusions are directly deduced from the equations.