Modeling and Simulation of Missiles in 6 DoF

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(410) 956-8805
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Modeling and Simulation of Missiles in 6 DoF

3-Day Course

$1990 per person


During three days I will provide a wide-ranging overview of high fidelity missile modeling. Starting with air-launched missiles against air and ground targets, followed by ground-launched missiles against ballistic missiles and aircraft, you will be introduced to the fundamental principles that govern all missile modeling.

We will derive the 6 DoF equations of motion using modern tensor flight dynamics, summarize coordinate systems, discuss the pros-and-cons of aerodynamic modeling, explain workable autopilots with several guidance laws, and offer detailed RF and IR sensor models. To put these models into action, I will demonstrate their integration into three 6 DoF simulations: AIM6, air-to-air missile simulation, AGM6 air-to-ground missile simulation, and SAM6 ground-to-air missile simulation.

Throughout the course I will run typical fly-out trajectories and project them on the screen. You may follow me on your own laptop with the provided source code and plotting programs (requires Windows operating system, Microsoft Visual C++ compiler, and administrative privileges.) These prototype simulations will enable you to jumpstart your 6 DoF simulation projects.

  • Modeling flight dynamics with tensors
  • Kinematics and dynamics of 6 DoF aerospace vehicles
  • Integration of missile subsystems: aerodynamics, propulsion, actuators, autopilots, guidance, seekers and navigation
  • Demonstration of missile 6DoF simulations in C++
  • How to build your own 6 DoF simulations

    Knowing how to assess and construct high fidelity simulations has become essential for any aerospace project.

  1. Concepts in Modeling with Tensors
    • Definitions, the M&S pyramid
  2. Matrices, Vectors, and Tensors
    • Invariant modeling with tensors
    • Definition of frames and coordinate systems
  3. Coordinate Systems
    • Heliocentric, inertial, geographic coordinate systems
    • Body, wind, flight path coordinate systems
  4. Kinematics of Flight Mechanics
    • Rotational time derivative
    • Euler transformation
  5. Six DoF Equations of Motion
    • Newton’s translational equations
    • Euler’s attitude equations
  6. Aerodynamic Modeling
    • In body axes
    • In aeroballistic axes
  7. Propulsion
    • Rocket, turbojet, and combined cycle propulsion
  8. Autopilots
    • Roll and heading controllers
    • Attitude controllers
    • Acceleration controllers
  9. Seekers
    • RF and IR sensors
  10. Guidance and Navigation
    • Line guidance, proportional navigation
    • Optimal guidance laws
  11. Six DoF Simulations in CADAC++
    • AIM6 Air intercept missile
    • AGM6 Air-to-ground missile
    • SAM6 Surface-to-air missile

Tuition for this three-day course is $1990 at one of our scheduled public courses. Onsite pricing is available. Please call us at 410-956-8805 or send an email to

Register Now Without Obligation.


Dr. Peter H. Zipfel founded Modeling and Simulation Technologies, which is devoted to consult and instruct in the functional integration of aerospace system using computer simulations. He authored the widely used text book “Modeling and Simulation of Aerospace Vehicle Dynamics”, and published three self-study course on missile and aircraft M and S.

Over 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 fifty years he created simulations of helicopters, missiles, aircraft, and hypersonic vehicles 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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