Related papers: Regularization of the circular restricted three-bo…
We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…
We present a method for solving trapped few-body problems and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical…
An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve…
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic…
The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a…
The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…
This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k…
The restricted four body problem studies the dynamics of a massless particle under the gravitational force produced by three masses (primaries) in an equilateral configuration. One primary, say m3, is considered too small compared with the…
An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…
In this paper we define a small variation of the Taylor method and a formula for the global error of this new numerical method that allows us to keep track of the round-off error and does not require previous knowledge of the exact…
We consider the Cahn-Hilliard equation with constant mobility and logarithmic potential on a two-dimensional evolving closed surface embedded in $\mathbb R^3$, as well as a related weighted model. The well-posedness of weak solutions for…
In this paper we regularize the Kepler problem on $S^3$ in several different ways. First, we perform a Moser-type regularization. Then, we adapt the Ligon-Schaaf regularization to our problem. Finally, we show that the Moser regularization…
Higher order normalizations are performed in the generalized photogravitational restricted three body problem with Poynting-Robertson drag. In this problem we have taken bigger primary as a source of radiation and smaller primary as an…
In the last decades a peculiar family of solutions of the Circular Restricted Three Body Problem has been used to explain the temporary captures of small bodies and spacecrafts by a planet of the Solar System. These solutions, which transit…
Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…
In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system…
In this paper, we consider the elliptic relative equilibria of four-body problem. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic relative equilibria of $4$-bodies splits into two independent linear…
This thesis starts from a review on current research on the local hypoellipticity of the $\bar\partial$-Neumann problem. It presents the classical method of regularity from estimates of the energy: subelliptic as well as superlogarithmic.…