Euler Angles and Quaternions in Six Degree of Freedom Simulations of Projectiles

Abstract

When developing simulations of aircraft, missiles or gun-launched projectiles, investigators require a coordinate frame in which to follow the motion. Newton's laws require an inertial (unaccelerated) frame. The earth is a convenient reference frame but is not inertial since the earth rotates. The earth may nonetheless be used, with Coriolis and centripetal accelerations included to account for the earth's rotation. However, the projectile is both translating and rotating. Thus it is convenient to express the equations of motion of the projectile, missile or aircraft in coordinates that move along with it in some way. The obvious choice is body- fixed coordinates. These coordinates are attached to the projectile or aircraft and roll, pitch and yaw with it. The reader familiar with gimbals or gyroscopes will recognize that these Euler angles of roll, pitch and yaw are equivalent to gimbal angles. In the case of a guided projectile, the seeker, rate sensor, accelerometers, and control mechanisms whether aerodynamic or reaction control all operate in and are easiest to describe in body-fixed coordinates.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1996
Accession Number
ADA417259

Entities

People

  • Michael J. Amoruso

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Angular Motion
  • Computer Simulations
  • Computers
  • Control Systems
  • Coordinate Systems
  • Earth Models
  • Engineering
  • Equations
  • Equations Of Motion
  • Euler Angles
  • Guided Projectiles
  • Molecular Mechanics Methods
  • Moment Of Inertia
  • New York
  • Projectiles
  • Simulations
  • Trajectories

Fields of Study

  • Physics

Readers

  • Aerodynamics/Aeronautics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Inertial Navigation Systems.