Abstract
In 1962, Yoshihide Kozai reported his findings on the secular dynamics of asteroids moving in orbits with high inclination and eccentricity. In contrast to the classic understanding of the stability of planetary motion in the solar system, Kozai showed that asteroids can significantly change their orbital shape over a long timescale in an oscillatory manner between nearly circular orbits and highly elliptic orbits. An anti-correlated variation between orbital inclination and eccentricity characterizes this oscillation. The importance of Kozai's work in understanding the dynamical evolution of various systems was recognized decades later, including the fields of irregular satellites of planets, Oort Cloud, extrasolar planets, binary star systems, type Ia supernovae, planet climate, merging black hole systems, and so on.