Related papers: Stepsize errors in the $N$-body problem: discernin…
We describe numerical tools for the stability analysis of extrasolar planetary systems. In particular, we consider the relative Poincare variables and symplectic integration of the equations of motion. We apply the tangent map to derive a…
A major goal of the BepiColombo mission to Mercury is the determination of the structure and state of Mercury's interior. Here the BepiColombo rotation experiment has been simulated in order to assess the ability to attain the mission goals…
The advance of the pericenter of the orbit of a test body around a massive body in general relativity can be calculated in a number of ways. In one method, one studies the geodesic equation in the exact Schwarzschild geometry and finds the…
Astronomical solutions provide calculated orbital and rotational parameters of solar system bodies based on the dynamics and physics of the solar system. Application of astronomical solutions in the Earth sciences has revolutionized our…
We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than…
Breakthroughs in our understanding of physical phenomena have traditionally followed improvements in instrumentation. Studies of the magnetic field of the Sun, and its influence on the solar dynamo and space weather events, have benefited…
We present a numerical treatment of the annual modulation of relic neutrinos due to the Sun's gravitational influence. Extending our previously developed N-1-body simulation framework from Milky Way scales to solar system dynamics, we model…
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a…
Wisdom--Holman (WH) methods are algorithms used as a basis for a wide range of codes used to solve problems in solar system and planetary dynamics. The problems range from the growth and migration of planets to the stability of the solar…
We numerically investigate the stability of exceptional periodic classical trajectories in rather generic chaotic many-body systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates…
We explore the regular or chaotic nature of orbits of stars moving in the meridional (R,z) plane of an axially symmetric time-dependent disk galaxy model with a central, spherically symmetric nucleus. In particular, mass is linearly…
The dynamical evolution of the solar system is chaotic with a Lyapunov time of only $\sim$5 Myr for the inner planets. Due to the chaos it is fundamentally impossible to accurately predict the solar system's orbital evolution beyond…
On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide…
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects…
We extend the formalism of a previous paper to include the effects of flybys and instantaneous perturbations such as supernovae on the long-term secular evolution of hierarchical multiple systems with an arbitrary number of bodies and…
The characteristics of the resonant disturbing function for an asteroid perturbed by a planet in circular orbit are discussed. The location of the libration centers and their dependence with the orbital elements of the resonant orbit are…
The architecture and evolution of planetary systems are shaped in part by stellar flybys. Within this context, we look at stellar encounters which are too weak to immediately destabilize a planetary system but are nevertheless strong enough…
The increasing threat raised by space debris led to the development of different mathematical models and approaches to investigate the dynamics of small particles orbiting around the Earth. Such models and methods strongly depend on the…
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…
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical…