## On the pitching and yawing motion of a spinning symmetric missile governed by an arbitrary nonlinear restoring moment |

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accurate for planar Aeronautics and Space angle of attack Angular momentum approximate solutions developed ARBITRARY NONLINEAR RESTORING arbitrary power series arbitrary restoring becomes exact circular motion conservative moment represented constants D-2135 National Aeronautics derived which involves due to spin elliptic integral Equation 13 equation 20 equations of motion Euler angles exact expression expression is least first-order approximation formula 29 formula 30 free-flight data frequency of oscillation gamma function infinite series involves an infinite Kirk Kryloff-Bogoliuboff technique Lagrangian least accurate limit of circular Maurice minimum resultant angle Moffett Field motion and becomes motion becomes circular NASA TECHNICAL NOTE odd function oscillation is derived OTS price parabola PITCHING AND YAWING planar motion power of angle present approximation present method Rasmussen and Donn sin2 solutions developed agree Space Administration SPINNING SYMMETRIC MISSILE superior to results SYMMETRIC MISSILE GOVERNED Taylor series TECHNICAL NOTE D-2135 TN D-2135 National YAWING MOTION