In many applications, it is of interest to perform static finite element analyses on freely floating bodies that are not in quasi-static equilibrium; airplanes and helicopters maneuvering in flight for example. This is particularly so if topology optimization (TO) is to be used, since TO with dynamic analyses can be very computationally expensive. The so-called inertia relief method, which essentially entails computing the rigid body inertia and subtracting it from the given loads to make the system of loads self-equilibrating, can sometimes be used to replace a dynamic analysis with a static, thus enabling the use of high-resolution TO. We derive the inertia relief method for elastic continua and obtain a static variational problem which require that we can suppress (linearized) rigid body motions without affecting the deformation. Three methods for doing this are investigated. Based on the static variational problem we consider maximizing stiffness using TO. Numerical examples show that all three methods for suppressing rigid body motion work, and indicate that optimal designs for freely floating structures undergoing rigid acceleration can differ significantly from designs optimized under static conditions. (C) 2019 Elsevier B.Y. All rights reserved.