Related papers: Equipotential Surfaces and Lagrangian points in No…
The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of such systems we have performed two-dimensional hydrodynamic simulations of the…
We investigate the stability of motion close to the Lagrangian equilibrium points L4 and L5 in the framework of the spatial, elliptic, restricted three- body problem, subject to the radial component of Poynting-Robertson drag. For this…
We formulate and solve by semi-analytic means the axisymmetric equilibria of relativistic self-similar disks of infinitesimal vertical thickness. These disks are supported in the horizontal directions against their self-gravity by a…
In a previous work (Pichardo et al. 2005), we studied stable configurations for circumstellar discs in eccentric binary systems. We searched for "invariant loops": closed curves (analogous to stable periodic orbits in time-independent…
Ocean flows are routinely inferred from low-resolution satellite altimetry measurements of sea surface height assuming a geostrophic balance. Recent nonlinear dynamical systems techniques have revealed that surface currents derived from…
The majority of extrasolar planets discovered to date have significantly eccentric orbits, some if not all of which may have been produced through planetary migration. During this process, any planets interior to such an orbit would…
We develop a fully nonlinear approximation to the short-wavelength limit of eccentric waves in astrophysical discs, based on the averaged Lagrangian method of Whitham (1965). In this limit there is a separation of scales between the rapidly…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
Several uniqueness results for non-compact complete stationary spacelike surfaces in an $n(\geq 3)$-dimensional Generalized Robertson Walker spacetime are obtained. In order to do that, we assume a natural inequality involving the Gauss…
We numerically investigate the dynamics of rotation of several close-in terrestrial exoplanet candidates. In our model, the rotation of the planet is disturbed by the torque of the central star due to the asymmetric equilibrium figure of…
This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Sere and to Coti-Zelati, Ekeland and Sere,…
In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…
A wide range of exoplanet and exomoon models are characterized by a finite average rigidity and a viscosity much lower than the typical values for terrestrials. Such semiliquid bodies may or may not have rigid crusts with permanent figures.…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but…
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by…
A point mass at the center of an ellipsoidal homogeneous fluid is used as a simple model to study the effect of rotation on the shape and external gravitational field of planets and stars. Maclaurin's analytical result for a homogenous body…
In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. At the same time, the symplectic…
In this paper, a hybrid Lagrangian-Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian…