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- W2430682213 abstract "We study the molecules of negative energy hypersurfaces of the Euler problem. As an application, we determine the knot types of periodic orbits: we show that for energies below the critical Jacobi energy, every doubly-covered periodic orbit in the regularized system is a torus knot. Moreover, we prove that in the Euler problem homoclinic orbits exist for all mass ratios and for all energies at which the Lyapunov orbit exists. In particular, the unstable and the stable manifolds of the Lyapunov orbit coincide with each other. Moreover, by means of the elliptic coordinates, we show that every homoclinic orbit rotates around one of the primaries precisely once." @default.
- W2430682213 created "2016-06-24" @default.
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- W2430682213 date "2016-06-17" @default.
- W2430682213 modified "2023-09-27" @default.
- W2430682213 title "Molecules of the Euler problem of two fixed centers and its applications" @default.
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