Six Degrees Of Freedom Modeling and Simulation of Aerospace Vehicle

Course Length:



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. Zipfel’s textbook “Modeling and Simulation of Aerospace Vehicle Dynamics”, 3rd Ed, 2014, published by AIAA.

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
  • Newton’s translational equations
  • Euler’s 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


REGISTRATION:  There is no obligation or payment required to enter the Registration for an actively scheduled course.   We understand that you may need approvals but please register as early as possible or contact us so we know of your interest in this course offering.

SCHEDULING:  If this course is not on the current schedule of open enrollment courses and you are interested in attending this or another course as an open enrollment, please contact us at (410)956-8805 or Please indicate the course name, number of students who wish to participate. and a preferred time frame. ATI typically schedules open enrollment courses with a 3-5 month lead-time.   To express your interest in an open enrollment course not on our current schedule, please email us at

For on-site pricing, you can use the request an on-site quote form, call us at (410)956-8805, or email us at

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