# Resonances and close approaches. I. The Titan-Hyperion case

@article{Bevilacqua1980ResonancesAC, title={Resonances and close approaches. I. The Titan-Hyperion case}, author={Roberto Bevilacqua and Ornella Menchi and Andrea Milani and Anna Maria Nobili and Paolo Farinella}, journal={The moon and the planets}, year={1980}, volume={22}, pages={141-152} }

AbstractThe orbits of Titan and Hyperion represent an interesting case of orbital resonance of order one (ratio of periods 3/4), which can be studied within a reasonable accuracy by means of the planar restricted three-body problem. The behaviour of this resonance has been investigated by numerical integrations, of which we show the results in terms of the Poincaré mapping in the plane of the coordinates η = ✓[(2L − 2G)] cos (
$$\tilde \omega $$
H − t)and ξ = −,✓[(2L − 2G)] sin (
$$\tilde…

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## References

SHOWING 1-10 OF 15 REFERENCES

### Instabilities in dynamical systems : applications to celestial mechanics : proceedings of the NATO Advanced Study Institute held at Cortina d'Ampezzo, Italy, July 30-August 12, 1978

- Physics, Geology
- 1979

I: Fundamental Considerations of Stability.- Simple Non-Integrable Systems with Two Degrees of Freedom.- Instabilities in Systems of Three Degrees of Freedom.- Perturbed Twist Maps, Homoclinic Points…

### Orbital Resonances in the Solar System

- Physics, Geology
- 1976

Orbital resonances are defined as any system of two or more satellites (including planets) orbiting the same primary and whose orbital mean motions are in a ratio of small whole numbers. Known…

### Evolution of satellite resonances by tidal dissipation.

- Physics
- 1973

Analysis of a realistic model shows how satellites' gravitational interaction can halt their differential tidal evolution when resonant commensurabilities of their orbital periods are reached. The…

### Differentiable dynamical systems

- Mathematics
- 1967

This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a…