Solving Nonlinear Aeronautical Problems Using the Carleman Linearization Method
Many problems in aeronautics can be described in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually nontrivial. This research will apply the Carleman linearization technique to three model problems: a two-degree-of-freedom (2DOF) ballistic trajectory, Blasius' boundary layer, and Van der Pol's equation and evaluate how well the technique can adequately approximate the solutions of these ordinary differential equations.