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# Accession Number:

## AD0002719

# Title:

## THE THEORY OF SPINNING SHELL

# Descriptive Note:

# Corporate Author:

## ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

# Report Date:

## 1952-11-01

# Pagination or Media Count:

##
40.0

# Abstract:

## The equations of motion of a symmetrical rigid body moving through a fluid are developed. The aerodynamic forces and torques are assumed to depend only on the position and orientation of the body and on its velocity and angular momentum, and to have the proper symmetry otherwise, they are general. A reduced problem is solved first, that of the motion, about its center of mass, of a top under a torque depending in a special way on the inclination of its axis. The equations of motion of the general problem are then transformed to equations of change of parameters which are constant for the reduced problem. The equations for secular change of the parameters lead to a problem of nonlinear dynamics which determines the stability of the yawing motion. The secular equations are obtained explicitly for a special variation of the aerodynamic forces and torques with yaw angle. For small yaw the results agree with the usual linearized theory.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#