Related papers: The Gravisphere Method Algorithm Programming
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural…
We have developed a general geometric treatment of the GCE valid for any stationary axisymmetric metric. The method is based on the remark that the world lines of objects rotating along spacely circular trajectories are in any case, for…
We investigate the behaviour of two recent methods for the computation of preliminary orbits. These methods are based on the conservation laws of Kepler's problem, and enable the linkage of very short arcs of optical observations even when…
In this paper we describe a method to estimate a neighborhood containing a periodic orbit of a given system of two ordinary differential equations. By using the theory of integral averages, the system of differential equations can be…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
In this study, we experimentally examine the behavior of a free-falling rigid sphere penetrating a quiescent liquid pool. Observations of the sphere trajectory in time are made using two orthogonally placed high-speed cameras, yielding the…
The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a…
Based on the recent finding that the difference in proper time of two clocks in prograde and retrograde equatorial orbits about the Earth is of the order 10^{-7}s per revolution, the possibility of detecting the terrestrial gravitomagnetic…
In celestial mechanics, proper orbits related to missions are obtained by solving two-point boundary value problems. Since a selection method of initial value affects the convergence of the solution, developing an effective method to find…
Computationally tractable methods are developed for centralized goal assignment and planning of collision-free polynomial-in-time trajectories for systems of multiple aerial robots. The method first assigns robots to goals to minimize total…
The emission of gravitational waves from a system of massive objects interacting on elliptical, hyperbolic and parabolic orbits is studied in the quadrupole approximation. Analytical expressions are then derived for the gravitational wave…
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…
Here we revisit an initial orbit determination method introduced by O. F. Mossotti employing four geocentric sky-plane observations and a linear equation to compute the angular momentum of the observed body. We then extend the method to…
In this paper we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector and a very short arc (VSA) of optical observations. Using the conservation laws of the two-body dynamics, we…
We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response. We achieve this by rewriting the interaction energy expression exclusively in terms of…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
A problem of constructing the trajectory of a spacecraft flight to Venus within the framework of a mission including landing of a lander in a given region of the planet's surface is being considered. A new celestial mechanics related method…
The emission of gravitational waves from a system of massive objects interacting on hyperbolic orbits is studied in the quadrupole approximation. Analytic expressions are derived for the gravitational radiation luminosity, the total energy…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…