  Using the Schwarzschild-type coordinates in stead of the global ones we
reconstruct the classical rotating closed string solutions in the AdS*5 x S*5
backgrounds. They are explicitly described by the Jacobi elliptic and
trigonometrical functions of worldsheet coordinates. We study the orbiting
closed string configurations in the near-horizon geometries of Dp, NS1 and NS5
branes, and derive the energy and spin of them, whose relation takes a simple
form for short strings. Specially in the D5 and NS5 backgrounds we have a
linear relation that the energy of the point-like string is proportional to the
spin, which is associated with the spectrum of strings in the pp-wave
geometries obtained by taking a special Penrose limit on the D5 and NS5
backgrounds.
