# Modeling and Simulation of Missiles in 6 DoF

Training Rocket Scientists Since 1984

(410) 956-8805
(888) 501-2100

## Modeling and Simulation of Missiles in 6 DoF

### Summary

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
• Attitude controllers
• Acceleration controllers
9. Seekers
• RF and IR sensors
• Optimal guidance laws
11. Six DoF Simulations in CADAC++
• AIM6 Air intercept missile
• AGM6 Air-to-ground missile
• SAM6 Surface-to-air missile

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

### Instructor

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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