FLIGHT MECHANICS: THEORY OF FLIGHT PATHS

Before specific performance problems can be analyzed, it is necessary
to build a foundation and derive general equations which are valid for
every problem. In this connection, the basic elements of kinematics and
dynamics are reviewed in Chapters 1 and 2 and then applied in Chapter 3
to derive the equations of motion for rocket-powered vehicles as well as
vehicles propelled by air-breathing jet engines. Special effort is devoted
to clarifying the basic concepts of thrust and aerodynamic force.

It is well known from Classical Mechanics that the translational motion
of a body is described by the equation of linear momentum while the
rotational motion is governed by the equation of angular momentum.
Although stability and control analyses require that the translational
and rotational motions be considered simultaneously, trajectory studies
can be simplified by means of engineering hypotheses whose effect is to
uncouple the equation of linear momentum from the equation of angular
momentum. In this connection, after the vectorial equations governing
the trajectory of a vehicle in both an inertial reference frame and a
reference frame rigidly associated with the Earth are established, the corresponding scalar equations are derived in Chapter 4 with reference to a
uniform gravitational field and in Chapter 5 with reference to a central
gravitational field. Although Volume I is concerned with the flat Earth
model only, the equations pertaining to flight over a spherical Earth are
included in order to make the general discussion complete.