Related papers: Explicit evolution relations with orbital elements…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a first-order secular theory that reproduces…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
Traditional analytical theories of celestial mechanics are not well-adapted when dealing with highly elliptical orbits. On the one hand, analytical solutions are quite generally expanded into power series of the eccentricity and so limited…
The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…
The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of…
Although mass transfer (MT) has been studied primarily in circular binaries, observations show that it also occurs in eccentric systems. We investigate orbital evolution during nonconservative MT in eccentric orbits, a process especially…
The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner…
Advances in the variational approach to the $n$-body problem have led to significant progress in celestial mechanics, uncovering new types of possible orbits. In this paper, critical points of the Lagrangian action associated with the…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
The parameterised post-Newtonian (PPN) formalism is a weak-field slow-motion approximation for both GR and some of its generalisations. It permits various parameterisations of the motion, among which are the Lagrange-type and Gauss-type…
Modern applications of celestial mechanics include the study of closely packed systems of exoplanets, circumbinary planetary systems, binary-binary interactions in star clusters, and the dynamics of stars near the galactic centre. While…
The secular Laplace-Lagrange orbital solution, decomposing eccentricities into a set of uniformly precessing eigenmodes is a classical result that is typically solved numerically. However, in the limit where orbits are closely spaced,…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…