(left) The characteristic curves of the planar family CR and the 3D family L02 (and its equivalent K02) of the ellipsoid. Blue (red) color indicates stability (instability). B2 is the vco where the two families intersect. (right) The characteristic curves for the corresponding families of 433-Eros potential. L02 and K02 are families of different orbits. The transition from the ellipsoid (left) to the mascon model of 433-Eros (right) indicates that scheme II takes place.

(left) The characteristic curves of the planar family CR and the 3D family L02 (and its equivalent K02) of the ellipsoid. Blue (red) color indicates stability (instability). B2 is the vco where the two families intersect. (right) The characteristic curves for the corresponding families of 433-Eros potential. L02 and K02 are families of different orbits. The transition from the ellipsoid (left) to the mascon model of 433-Eros (right) indicates that scheme II takes place.

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In Karydis et al. (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What’s more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction...

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Context 1
... II holds true for the case of v.c.o. B 2 of the ellipsoid from which the 3D families L 02 and K 02 originate (see Paper I). The two families are equivalent because they consist of the same doubly symmetric periodic orbits but their characteristic curves are presented in different spaces of initial conditions. In the left panel of Fig. 4, we present the initial conditions of the orbits in K 02 family. As we have already mentioned, the C R family of 433-Eros shows an unstable segment at B 2 , defined by the points B 21 and B 22 . These points should be bifurcation points of other families. By computing the families K 02 and L 02 in the asymmetric potential of 433-Eros ...
Context 2
... the initial conditions of the orbits in K 02 family. As we have already mentioned, the C R family of 433-Eros shows an unstable segment at B 2 , defined by the points B 21 and B 22 . These points should be bifurcation points of other families. By computing the families K 02 and L 02 in the asymmetric potential of 433-Eros (see right panel of Fig. 4) we obtain that i) the two families are separated and they now consist of different asymmetric periodic orbits ii) the families pass from the points B 21 and B 22 and, therefore, the continuation scheme II is valid here. K 02 consists of unstable orbits and L 02 of stable ones (at least in the neighborhood of the bifurcation points). ...