Related papers: Higher Order Approximation to the Hill Problem Dyn…
We present an extension of an algorithm for the classical scalar $p$-Laplace Dirichlet problem to the vector-valued $p$-Laplacian with mixed boundary conditions in order to solve problems occurring in shape optimization using a $p$-harmonic…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
The goal of this article is to study closed connected sets of periodic solutions, of autonomous second order Hamiltonian systems, emanating from infinity. The main idea is to apply the degree for SO(2)-equivariant gradient operators defined…
Driven by the desire to find positions that satisfy keepout constraints for a space-based telescope mission, this work develops a process for tracing a point in space in the regime of the restricted three-body problem to a halo orbit,…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
Recently we derived the next-to-next-to-leading order post-Newtonian Hamiltonians at spin-orbit and spin(1)-spin(2) level for a binary system of compact objects. In this talk the derivation of them will be shortly outlined at an…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare…
A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the…
Recent gravitational wave (GW) detections showing signatures of eccentricity and spin precession underscore the need to model binary black holes (BBHs) possessing these features simultaneously. Most efforts over the past fifteen years to…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
We study the dynamics in the neighborhood of the collinear Lagrangian points in the spatial, circular, restricted three--body problem. We consider the case in which one of the primaries is a radiating body and the other is oblate (although…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
A pseudo-Newtonian Hill problem based on the Paczynski-Wiita pseudo-Newtonian potential that reproduces general relativistic effects is presented and compared with the usual Newtonian Hill problem. Poincare maps, Lyapunov exponents and…
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular,…
We employ one-loop scattering amplitudes in Einstein-Maxwell theory to compute the classical Hamiltonian of a binary system of two charged, non-spinning compact objects. The Hamiltonian is valid to all orders in velocity and up to second…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…