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Six Degrees of Freedom Modeling of Missile and Aircraft Simulations

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Technical Training Short On Site Course Quote

This is a two-day course. As modeling and simulation (M&S) is penetrating the aerospace sciences at all levels, this course will introduce you to the difficult subject of modeling aerospace vehicles in six degrees of freedom (6 DoF). Starting with the modern approach of tensors, the equations of motion are derived and, after introducing coordinate systems, they are expressed in matrices for compact computer programming. Aircraft and missile prototypes will exemplify 6 DoF aerodynamic modeling, rocket and turbojet propulsion, actuating systems, autopilots, guidance, and seekers. These subsystems will be integrated step by step into full-up simulations. For demonstrations, typical fly-out trajectories will be run and projected on the screen. The provided source code and plotting programs let you duplicate the trajectories on your PC (requires MS Visual C++ compiler, free Express version). Based on these prototype simulations you can build your own 6 DoF aerospace simulations.

Attendees receive all course slides, the C++ source code of the aircraft and missile simulations, and access to the full CADAC++ simulation framework and plotting software used in this course. It is recommended, though not required, that the attendees bring with them Dr. Zipfelís textbook "Modeling and Simulation of Aerospace Vehicle Dynamics", 3rd Ed, 2014, published by AIAA.

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Dr. Peter Zipfel is a graduate of the University Stuttgart, Germany, and the Catholic University of America with a Ph.D. in aerospace engineering. He founded Modeling and Simulation Technologies, which advises and instructs functional integration of aerospace systems using computer simulations. For 35 years he taught courses in modeling and simulation, guidance and control, and flight dynamics at the University of Florida and over the span of 45 years he created aerospace simulations for the German Helicopter Institute, the U.S. Army, and U.S. Air Force. He is an AIAA Associate Fellow and an internationally recognized short course instructor.

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What You Will Learn

  • How to model flight dynamics with tensors
  • How to formulate the kinematics and dynamics of 6 DoF aerospace vehicles
  • Functional integration of aircraft and missile subsystems: Aerodynamics, propulsion, actuators, autopilots, guidance, seekers and navigation
  • See in action aircraft and missile 6DoF simulations
  • How to build your own 6 DoF simulations

Course Outline:

  • Concepts in Modeling with Tensors
  • Definitions, the M&S pyramid
  • Matrices, Vectors, and Tensors
  • Invariant modeling with tensors
  • Definition of frames and coordinate systems
  • Coordinate Systems
  • Heliocentric, inertial, geographic coordinate systems
  • Body, wind, flight path coordinate systems
  • Kinematics of Flight Mechanics
  • Rotational time derivative
  • Euler transformation
  • Equations of Motion of Aircraft and Missiles
  • Newtonís translational equations
  • Eulerís attitude equations
  • Aerodynamics of Aircraft and Missiles
  • Aircraft aerodynamics in body coordinates
  • Missile aerodynamics in aeroballistic coordinates
  • Propulsion
  • Rocket, turbojet and combined cycle propulsion
  • Autopilots for Aircraft and Missiles
  • Roll and heading autopilots
  • Attitude autopilots
  • Acceleration autopilots
  • Seekers for Missiles
  • Radar and IR sensors
  • Guidance and Navigation
  • Line guidance, proportional navigation
  • Optimal guidance laws


This course is not on the current schedule of open enrollment courses. If you are interested in attending this or another course as open enrollment, please contact us at (410) 956-8805 or at and indicate the course name and number of students who wish to participate. ATI typically schedules open enrollment courses with a lead time of 3-5 months. Group courses can be presented at your facility at any time. For on-site pricing, request an on-site quote. You may also call us at (410) 956-8805 or email us at

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