Related papers: A differentiable N-body code for transit timing an…
The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation…
Trajectory prediction (TP) is crucial for ensuring safety and efficiency in modern air traffic management systems. It is, for example, a core component of conflict detection and resolution tools, arrival sequencing algorithms, capacity…
The gravitational N-body simulation in the Solar system was performed using different parallel approaches with the comparisons in the computational times and speed-up values being carried out under different model sizes and the number of…
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…
Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment…
Modelling the cosmic large-scale structure can be done through numerical N-body simulations or by using perturbation theory. Here, we present an N-body approach that effectively implements a multi-step forward model based on Lagrangian…
Elegant integration schemes of second and fourth order for simulations of rigid body systems are presented which treat translational and rotational motion on the same footing. This is made possible by a recent implementation of the exact…
The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time…
Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with…
In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to…
We address the generation of initial conditions (ICs) for GRAMSES, a code for nonlinear general relativistic (GR) $N$-body cosmological simulations recently introduced in Ref. [1]. GRAMSES adopts a constant mean curvature slicing with a…
The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the…
Quantum-corrected equations of motion generically contain higher time derivatives, computed here in the setting of canonically quantized systems. The main example in which detailed derivations are presented is a general anharmonic…
The code we describe (FLY) is a newly written code (using the tree N-body method), for three-dimensional self-gravitating collisionless systems evolution. FLY is a fully parallel code based on the tree Barnes-Hut algorithm and periodical…
A significant challenge in manipulation motion planning is to ensure agility in the face of unpredictable changes during task execution. This requires the identification and possible modification of suitable joint-space trajectories, since…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
Creating software dedicated to simulation is essential for teaching and research in Science, Technology, Engineering, and Mathematics (STEM). Physics lecturing can be more effective when digital twins are used to accompany theory classes.…
We present a new implementation of the numerical integration of the classical, gravitational, N-body problem based on a high order Hermite's integration scheme with block time steps, with a direct evaluation of the particle-particle forces.…
We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…
In this paper, we describe procedures for computing higher-order time derivatives of the Lie-group Newton-Euler, Articulated-Body Inertia, and hybrid dynamics algorithms for floating-base trees, where the base configuration evolves on SE(3)…