The variations of lift and pitching moment with sideslip in supersonic flow have been calculated for a representative gorup of plan forms. The variations of lift and pitching moment with aspect ratio and Mach number at zero sideslip were also investigated. The analysis was based on linearized potential theory and was applied to triangular, trapezoidal, rectangular, and swept-back plan forms without dihedral.

The theoretical lift and pitching moment due to angle of attack and pitching and the lateral force and yawing moment due to rolling of a trapezoidal wing are derived. The equations are applicable when the inboard Mach line from a leading-edge tip intersects the trailing edge and the outboard Mach line lies ahead of the side edge. When the side edges are raked in, the former condition is sufficient. A comparison based on theoretical expressions of the lift and rolling effectiveness for half-delta tip (point forward) and trailing-edge flaps on various plan forms is made.

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.