<DOC>
<DOCNO>
639
</DOCNO>
<TITLE>
analytical study of the tumbling motions of vehicles
entering planetary atmospheres .
</TITLE>
<AUTHOR>
tobak,m.
</AUTHOR>
<BIBLIO>
nasa tn.d1549, 1962.
</BIBLIO>
<TEXT>
  the tumbling motion of vehicles
entering planetary atmospheres is
analyzed .  a differential equation
governing the tumbling motion, its
arrest, and the subsequent oscillatory
motion is obtained and identified
as the equation for the fifth painleve
transcendant .  an approximate
analytical solution for the transcendant
is derived .  comparisons with
results obtained from numerical
integration of the exact equations of
motion indicate that the solution for the
angle-of-attack history is
sufficiently accurate to be of practical use .
</TEXT>
</DOC>
