## A nonlinear theory for sonic-boom calculations in a stratified atmosphereThe exact solutions to the equations of gas dynamics are given with respect to the axis of slender lifting bodies in a stratified atmosphere. The boundary condition is satisfied by using slender-body theory. The solution predicts the magnitude of the pressure rise of the sonic boom and estimates the nonlinear effects in the vicinity of the cutoff point. |

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abscissa According to equation altitude of flight angle of attack angle of inclination body of revolution boundary condition bow shock caustic characteristic surface characteristic variable constant coordinates cp D^cp cp Drw cutoff point denotes differential equations due to gravity enthalpy entropy equa equation is written equation of continuity equations 15 first-order calculal Fourier series function of integration generatrix ground homentropic independent variables integration function irrotational Langley Research Center large distances locally dependent basis Mach cone Mach number NASA NONLINEAR THEORY number of degrees orders of magnitude partial differential equations perturbation pressure rise pressure signatures previous paper ref reflected wave rewritten second-order angle shock front signatures at various slender lifting bodies slender-body theory solved for large SONIC-BOOM CALCULATIONS speed of sound stratified atmosphere streamline subscript superscript supersonic flow undisturbed flow unknown functions velocity vector w x curl wave is reflected wave normal cone weak shocks zeroth order zeroth-order