Related papers: Looking for Stable Celestial Systems Using Bayesia…
We consider the constrained stabilization problem of second-order systems evolving on the n-sphere. We propose a control strategy with a constraint proximity-based dynamic damping mechanism that ensures safe and almost global asymptotic…
Designing spacecraft trajectories remains challenging in the presence of stochastic effects such as maneuver execution errors and observation uncertainties. Although covariance control and belief-space planning provide useful tools for…
We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and…
In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We carry out more than 3 10^8 numerical simulations of planets between the size of Mercury and…
This paper describes design of the trajectory and analysis of the stability of collinear point $L_2$ in the Sun-Earth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the…
The method originally developed by Kalnajs for the numerical linear stability analysis of round galactic disks is implemented in the regimes of non-analytic transformations between position space and angle-action space, and of vanishing…
The stability of the motion of the planet satellites is considered in the model of the general three-body problem (Sun-planet-satellite). "Sundman surfaces" are constructed, by means of which the concept "Sundman stability" is formulated.…
Optimal error estimates of stable and stabilized Lagrange-Galerkin (LG) schemes for natural convection problems are proved under a mild condition on time increment and mesh size. The schemes maintain the common advantages of the LG method,…
Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes,…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters…
Two types of stability boundaries exist for any planetary system consisting of one star and two planets. Lagrange stability requires that the planets remain bound to the star, conserves the ordering of the distance from the star, and limits…
In this work, an innovative data-driven moving horizon state estimation is proposed for model dynamic-unknown systems based on Bayesian optimization. As long as the measurement data is received, a locally linear dynamics model can be…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
Spatial perception is a key task in several machine intelligence applications such as robotics and computer vision. In general, it involves the nonlinear estimation of hidden variables that represent the system's state. However, in the…
Sample efficiency is one of the key factors when applying policy search to real-world problems. In recent years, Bayesian Optimization (BO) has become prominent in the field of robotics due to its sample efficiency and little prior…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…