Abstract
We investigate the topological types and bifurcations of periodic orbits in the gravitational field of irregular bodies by the well-known two parameter analysis method. Results show that the topological types of periodic orbits are determined by the locations of these two parameters and that the bifurcation types correspond to their variation paths in the plane. Several new paths corresponding to doubling period bifurcations, tangent bifurcations and Neimark–Sacker bifurcations are discovered. Then, applications in detecting bifurcations of periodic orbits near asteroids 101955 Bennu and 2867 Steins are presented. It is found that tangent bifurcations may occur three times when continuing the vertical orbits near the equilibrium points of 101955 Bennu. The continuation stops as the Jacobi energy reaches a local maximum. However, while continuing the vertical orbits near the equilibrium points of 2867 Steins, the tangent bifurcation and pseudo period-doubling bifurcation occur. The continuation can always go on, and the orbit ultimately becomes nearly circular.
Highlights
Exploring small bodies such as asteroids and comets has become a hot area since the first flyby mission of (951) Gaspra by the Galileo spacecraft in 1991 [1]
Applications of Lyapunov, axial and vertical orbits in the Earth–Moon system were computated by Dichmann et al [14], Parker and Lo [15] made use of planar periodic orbits and their invariant manifolds in the circular restricted three-body problem to design transfer orbits, Jiang et al [16] investigated the stable orbits of spacecraft near small bodies and Lian [17] studied the dynamics and control of a tetrahedral spacecraft formation near the Sun–Earth L2 point
An investigation of topological types and bifurcations of periodic orbits from a global point of view was conducted in this work
Summary
Exploring small bodies such as asteroids and comets has become a hot area since the first flyby mission of (951) Gaspra by the Galileo spacecraft in 1991 [1]. To obtain a global picture of the topological structures and bifurcation types of periodic orbits near asteroids, we use the “two parameter analysis” method. This method is mainly based on the symplectic property of monodromy matrix. As far as we can see, Broucke [30] applied this method to investigate the bifurcations of periodic orbits in the elliptic restricted three-body problem Based on this method, many studies about the three-body problem have been conducted, see, for example, Zagouras and Markellos [31], Papadakis and Zagouras [32], Kalantonis [33], etc. Bifurcation types and topological transitions during the numerical continuation of periodic orbits are investigated
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