Related papers: A differentiable N-body code for transit timing an…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of…
We introduce here our new approach to modeling particle cloud evolution off surface of small bodies (asteroids and comets), following the evolution of ejected particles requires dealing with various time and spatial scales, in an efficient,…
We design an accurate orbital integration scheme for the general N-body problem preserving all the conserved quantities but the angular momentum.This scheme is based on the chain concept (Mikkola & Aarseth 1993) and is regarded as an…
If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper we present a set of recurrence…
Gas-poor galaxies can be modelled as composite collisionless stellar systems, with a dark matter halo and one or more stellar components, representing different stellar populations. The dynamical evolution of such composite systems is often…
In most current debris disc models, the dynamical and the collisional evolutions are studied separately, with N-body and statistical codes, respectively, because of stringent computational constraints. We present here LIDT-DD, the first…
The time-symmetric block time--step (TSBTS) algorithm is a newly developed efficient scheme for $N$--body integrations. It is constructed on an era-based iteration. In this work, we re-designed the TSBTS integration scheme with dynamically…
An accurate and efficient method dealing with the few-body dynamics is important for simulating collisional N-body systems like star clusters and to follow the formation and evolution of compact binaries. We describe such a method which…
$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or…
We introduce Gradus.jl, an open-source and publicly available general relativistic ray-tracing toolkit for spectral modelling in arbitrary spacetimes. Our software is written in the Julia programming language, making use of forward-mode…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other…
Orbital motion of a body can be found from Newtonian equation of motion. However, it is useful to express the motion through time derivatives of Keplerian orbital elements, mainly if the motion is perturbed by small perturbing force. The…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…
We analytically work out the long-term, i.e. averaged over one orbital revolution, time variations of some direct observable quantities Y induced by classical and general relativistic dynamical perturbations of the two-body pointlike…
Over the past few years, robotics simulators have largely improved in efficiency and scalability, enabling them to generate years of simulated data in a few hours. Yet, efficiently and accurately computing the simulation derivatives remains…
We introduce a numerical method to integrate tidal effects on collisional systems, using any definition of the external potential as a function of space and time. Rather than using a linearisation of the tidal field, this new method follows…
In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby…
In early Solar System numerical simulations, where chaos is a primary driver, it is difficult to explore parameter space in a systematic way. In such simulations, stable configurations are hard to come by, and often require special…