ANALYTICAL SOLUTIONS FOR THE LINEAR AND NONLINEAR YAWING MOTION IN DENSE MEDIA

摘要

Analytical solutions for the linear and nonlinear yaw growth of a projectile impacting and traversing dense media are presented. From the linear solution, it is shown that Roecker's linear exponential yaw growth model can be obtained from the general solution for arbitrary impact yaw and yawing rates after a sufficient depth of penetration. However, using the general solution, it is shown that Roecker's yaw growth model does not adequately represent the yaw growth during the initial phase of the penetration event. Analytical solutions for the nonlinear yaw growth are then presented. For the particular form of the overturning moment considered here, the nonlinear yaw growth is characterized by oscillating motion at yaw angles less than 180 degrees or by an end-over-end tumbling motion, depending on the striking yaw and yawing rate. A limiting case motion between the two regimes is also possible but physically unlikely. However, the limiting case motion represents an approximation of the nonlinear exponential yaw growth over a significant portion of the penetration event for the general case, provided the striking yaw and yawing rate are small. This validates its use as a representation for the nonlinear yaw growth in prior work.