Application of the Laplace Transformation to the Solution of the Lateral and Longitudinal Stability Equations

The application of the Laplace transformation to the solution of the lateral and longitudinal stability equations is presented. The expressions for the time history of the motion in response to a sinusoidal control motion are derived for the general case in which the initial conditions, initial displacements and initial velocities, are assumed different from zero. Some illustrative examples of the application of the Laplace transform to ordinary linear differential equations with constant coefficients and a number example of a specific problem are presented in appendixes.