guidance, flight mechanics and trajectory optimization

where the final time tf may or may not be specified. The initial state is
assumed specified with
AT t=i,
If #l%f, $1 is zero in Eq. (2.4.84) the Problem of Bolza reduces to the
problem of Lagrange. If k(x,u) is zero the Mayer problem results. The
type of physical situation which is implied by such a problem is illustrated
in the following two examples.
Example (1) - Simple Guidance Problem
Consider the problem of maneuvering a
rocket over a flat, airless earth
which was treated in Section
(2.2.2.3). The equation of motion in
this case becomes
f
I Sketch (2.4.5)
where x and y represent the horizontal and vertical position, m the
mass, 1/ the exhaust velocity (a constant), and ul and u2 are control
variables denoting the throttle setting and steering angle. Since the
thrust varies between zero and some maximum value, Tmax, the throttle
setting ul must satisfy the inequality
(2.4.86)
(2.4.88)
(2.4.89)
0 LU, L-/ (2.4.90)
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