Collision and annihilation of relative equilibrium points around asteroids with a changing parameter

摘要: In this work, we investigate the bifurcations of relative equilibria in gravitational potential asteroids. A theorem concerning a conserved quantity, which is about eigenvalues and number equilibria, presented proved. The quantity can restrict non-degenerate an asteroid. It concluded that field asteroid varies pairs odd number. addition, also kinds when parameter varies. Furthermore, studies have shown there exist transcritical bifurcations, quasi-transcritical saddle-node saddle-saddle binary supercritical pitchfork subcritical for found 216 Kleopatra, rotation period as parameter, changes from 7 to 5 3 1, are bifurcations.