Related papers: Design of distant retrograde orbits based on a hig…
Although Neural Differential Equations have shown promise on toy problems such as MNIST, they have yet to be successfully applied to more challenging tasks. Inspired by variational methods for image restoration relying on partial…
This study is aimed at answering the famous question of how the approximation errors at each iteration of Approximate Dynamic Programming (ADP) affect the quality of the final results considering the fact that errors at each iteration…
Exact and approximate analytical formulas are derived for the internal structure and global parameters of the spherical non-rotating quasi-incompressible planet. The planet is modeled by a polytrope with a small polytropic index n << 1, and…
High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
This work focuses on providing closed form analytical expressions to define frozen orbits under the effects of the zonal harmonics of an Earth-like planet. Particularly, the perturbation effects from the terms J2, J3, J4, J5, J6, and J7 are…
An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary…
Neural stochastic differential equation model with a Brownian motion term can capture epistemic uncertainty of deep neural network from the perspective of a dynamical system. The goal of this paper is to improve the convergence rate of the…
The classical disturbing function of the three-body problem widely used in planetary dynamics studies is an expansion of the gravitational interaction of the three-body problem with respect to zero eccentricity and zero inclination. This…
This work presents an analytical perturbation method to define and study the dynamics of frozen orbits under the perturbation effects produced by the oblatness of the main celestial body. This is done using a perturbation method purely…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We investigate the stability of prograde versus retrograde planets in circular binary systems using numerical simulations. We show that retrograde planets are stable up to distances closer to the perturber than prograde planets. We develop…
The success of deep learning over the past decade mainly relies on gradient-based optimisation and backpropagation. This paper focuses on analysing the performance of first-order gradient-based optimisation algorithms, gradient descent and…
In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
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…
For an analytic differential system in $\mathbb R^n$ with a periodic orbit, we will prove that if the system is analytically integrable around the periodic orbit, i.e. it has $n-1$ functionally independent analytic first integrals defined…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…