Related papers: Symplectic map description of Halley's comet dynam…
Using methods from symplectic geometry, the second and fifth authors have provided theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their bifurcations in families, for the purpose of space mission…
The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this…
Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on…
Wisdom-Holman (WH) integrators are symplectic operator-splitting methods widely used for long-term N-body simulations of planetary systems. Most implementations use either Jacobi coordinates or democratic heliocentric coordinates (DHC) for…
We present new analyses of the photometric lightcurve of Comet 1P/Halley during its 1985/86 apparition. As part of a world-wide campaign coordinated by the International Halley Watch (IHW), narrowband photometry was obtained with telescopes…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
The Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) records line-of-sight Dopplergram images of convective flows on the surface. These images are used to obtain the multi-scale convective spectrum. We design…
In this study, the classical two-dimensional potential $V_N=\frac{1}{2}\,m\,\omega^2\,r^2 + \frac{1}{N}\,r^N\,\sin(N\,\theta)$, $N \in {\mathbb Z}^+$, is considered. At $N=1,2$, the system is superintegrable and integrable, respectively,…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
We present the current standing of an investigation into the structure of the Milky Way. We use smoothed particle hydrodynamics (SPH) to simulate the ISM gas in the Milky Way under the effect of a number of different gravitational…
The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters.…
We make an observation about Galilean transformation on a 1-D mass variable systems which leads us to the right way to deal with mass variable systems. Then using this observation, we study two-bodies gravitational problem where the mass of…
We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the…
Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a quantizable, compact, symplectic manifold $(M,\omega)$. We prove the existence of an action integral around loops in $\text{Ham(M)}$, and determine the value of this…
Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…
Using a recently developed two-scale formalism to determine the magnetic helicity spectrum (Brandenburg et al. 2017), we analyze synoptic vector magnetograms built with data from the Vector Spectromagnetograph (VSM) instrument on the…
Symplectic maps are routinely used to describe single-particle dynamics in circular accelerators. In the case of a linear accelerator map, the rotation number (the betatron frequency) can be easily calculated from the map itself. In the…
In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We…