Euler’s Law

Rapidly we reach the climax of Part 1. Its first pillar is Newton’s second law, expressing the translational dynamics of aerospace vehicles using the linear mo­mentum. With the angular momentum defined we are prepared to formulate Euler’s law, the second pillar of flight dynamics.

We will begin with a historical argument that splits the dynamicists into two camps, the Newtonians and the Eulerians, though the consequences for modeling and simulation are zilch. The particle again will serve the elemental formulation, from which we derive two forms of Euler’s law. Most important for us is thefree – flight exposition, serving all aerospace vehicle applications. The other form, the spinning top with one point fixed, is more of historical and academic significance. Dealing with clustered bodies will be a venture for us. Fortunately, most air – and spacecraft contain spinning bodies with fixed mass centers. These arrangements can be treated in a straightforward manner. For moving bodies the formulation of Euler’s equation gives us access to many challenging modeling tasks.