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Simulation Implementation
When implementing Newton’s law on the computer, you have to answer many practical questions. What type of vehicle is being simulated: aircraft, missile, or satellite; is it flying near Earth or at great altitudes and hypersonic speeds; does the customer require high accuracy trajectory information or is he only interested in a quick, first-cut study? The answers determine the fidelity of your model.
The fidelity of a simulation is categorized according to the number of DoF it models. A rigid body, moving through air or space has six DoF, three translational and three rotational degrees. Newton’s law models the three translational degrees of freedom of the vehicle’s c. m., whereas Euler’s law (see next chapter) governs the three rotational degrees of freedom. Both together provide the highest fidelity.
However, for preliminary trajectory studies it may be adequate to model the vehicle as a particle. Only the translational equations apply, and the simulation is called a three-DoF model. If attitude motions have to be included, but a complete database is lacking, an interim model, the so-called pseudo-five-DoF simulation is used to great advantage. Two attitude motions, either pitch-yaw or pitch-bank, augment the three translational degrees of freedom. However, the attitude motions are not derived from Euler’s law, but from linearized autopilot responses. Ultimately, the full attitude motions, governed by Euler’s law, joined by Newton’s translational DoF form the full six-DoF simulations.
Besides fidelity requirements the form of the inertial frame categorizes a simulation. Interplanetary travel demands the heliocentric frame; Earth-orbiting or hypersonic vehicles use the J2000 inertial frame; and slow, Earth-bound vehicles can compromise with the Earth as an inertial frame.
I will summarize the more important versions of Newton’s translational equations, as they are employed in aerospace simulations. I will give you a glimpse of each category: three, five, and six degrees of freedom later. Chapters 8, 9, and 10 will provide the details.
