THE THEORY OF SPINNING SHELL

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1952
Accession Number
AD0002719

Entities

People

  • L. H. Thomas

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Aerodynamic Forces
  • Air Force
  • Air Force Facilities
  • Angular Momentum
  • California
  • Cartesian Coordinates
  • Chemical Engineering
  • Coefficients
  • Coordinate Systems
  • Equations
  • Equations Of Motion
  • Jet Propulsion
  • Momentum
  • Munitions
  • Nonlinear Dynamics
  • Ordnance Laboratories
  • Projectiles

Fields of Study

  • Mathematics
  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.