Related papers: Computing secular motion under slowly rotating qua…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
The main subject of this work is the study of the problem of the Trojan orbits from a perturbative Hamiltonian perspective. We face this problem by introducing first a novel Hamiltonian formulation, exploiting the well-differentiated…
Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called "relativistic corrections", computed with the required precision using the Post-(Post-)Newtonian formalism. The current…
We derive octupole-level secular perturbation equations for hierarchical triple systems, using classical Hamiltonian perturbation techniques. By extending previous work done to leading (quadrupole) order to octupole level (i.e., including…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…
We present a closed system of coupled first order differential equations governing the secular linear momentum loss of a compact binary due to emitted gravitational waves, with the leading order relativistic and spin-orbit perturbations…
In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital…
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The dominantly orbital state description is applied to the study of light mesons. The effective Hamiltonian is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement.…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
Two-body matrix elements of arbitrary local interactions are written as the sum of separable terms in a way that is well suited for the exchange and pairing channels present in mean-field calculations. The expansion relies on the…
We consider the solid-solid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the…
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the…