This is the Atoll, an air-to-air missile of the former Soviet Union.
Atoll is the NATO code name for the Soviet K-13, a copy of the U.S.
Sidewinder air-to-air, heat-seeking missile. Atoll originated in 1958, when
a Sidewinder fired from a Taiwanese F-86 fighter in the Taiwan Strait
lodged in an aircraft of the People's Republic of China but did not
China recovered the missile intact and turned it over to the Soviet Union,
which copied the design, mass-produced the missile, and exported Atolls to
its client states. The Atoll has the same basic dimensions as the
Sidewinder but has been modified over the years and is still in use. This
object was donated to the Smithsonian in 1993 by the U.S. Air Force.
Photo 154s, Smithsonian Udvar-Hazy Center, May 2013