<DOC>
<DOCNO>
499
</DOCNO>
<TITLE>
a closed-form solution for the oscillations of a vehicle
entering a planetary atmosphere .
</TITLE>
<AUTHOR>
greensite,a.l.
</AUTHOR>
<BIBLIO>
j. ae. scs. 29, 1962, 745.
</BIBLIO>
<TEXT>
  author considers the equation of the yawing motion of a missile,
derived with a series of customary assumptions and with the distance
traveled as the independent variable .  his assumptions include
the linearity of the aerodynamic forces, the constancy of the
aerodynamic coefficients with respect to mach number, the absence
of spin, and the absence of gravity .  if to these assumptions
one could add the common ballistic assumption of a constant air
density, the coefficients of this equation would have been condamped
sinusoids .  in ballistics any slow variation of these coefstant,
and the solution would have been simply the exponentiallyficients
is usually treated by adding an approximate correction
term to the damping rate (which is spoken of as the wkb perturbation)
.  however, with a body entering the planetary atmosphere the
variation of the air density is apparently of greater essence (this
is a point not stated explicitly in this brief communication), and
the equation is of the type .
the author shows that with a series of further transformations
the equation can be reduced to the form
the solutions of which are confluent hypergeometric
functions .  these functions are defined as series involving
gamma functions, and with a series of further assumptions
can be reduced to laguerre polynomials and bessel functions .
  it is certainly nice to have an exact solution to a problem which
has heretofore been extensively treated by approximations and by
the numerical approach .  this reviewer is puzzled, however, as to
the practical significance of the proposed approach .  an idealization
is of value in that it facilitates our understanding,. and the
numerical approach, in that it allows refinements of the problem,
freeing us from the necessity of idealizing .  but the proposed solution
is certainly more difficult to refine than the original problem,.
and it is certainly not simple (the solution of the original
equation is not the value of z, but the various /reverse/ transformations
of z) .  an evaluation of a series in practice must compete
with the numerical approach,. and the equation suggested is of the
zero) .  viewing the problem /afresh/ (in the light of the /computer
revolution/ and without the constraints imposed by the prior
art), it seems at least equally easy to /standardize/ the solutions
of the original equation .
</TEXT>
</DOC>
