Equations of Motion

Before Newton’s law can be applied, the choice of the inertial frame must be made. In Chapter 5 we discussed the options and Chapter 3 defined the frames. Most Earth-bound simulations use the J2000 inertial frame (see Sec. 3.1.2.2) or sometimes the Earth itself for vehicles that hug the ground. We shall focus on the J2000 frame to support the equations of motion for rockets and hypersonic vehicles. En passant, I will point out the simplifications that lead to the formulation over a flat Earth.

The derivation of the Cartesian approach is straightforward. The inertial position and velocity coordinates are directly integrated, and the forces, given in flight-path coordinates, are transformed to inertial coordinates.

The polar approach is used to track the effects of the Coriolis and centrifugal accelerations. Newton’s law is transferred to the rotating Earth frame and expressed in flight-path coordinates. No transformation is necessary for the forces.