Results 11 to 20 of about 783,055 (280)
Numerical integration in celestial mechanics: a case for contact geometry [PDF]
Celestial mechanics & dynamical astronomy, 2019 Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to such class. In this work we start an investigation of these models from the point of
M. Seri +3 more
arxiv +4 more sources
Degenerate billiards in celestial mechanics [PDF]
Regular and Chaotic Dynamics, 2017, 2016 In an ordinary billiard trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is degenerate. Degenerate billiards appear as limits of systems with singularities in celestial mechanics.
S. Bolotin
arxiv +3 more sources
celmech: A Python Package for Celestial Mechanics [PDF]
Astronomical Journal, 2022 We present celmech, an open-source Python package designed to facilitate a wide variety of celestial mechanics calculations. The package allows users to formulate and integrate equations of motion incorporating user-specified terms from the classical ...
S. Hadden, D. Tamayo
semanticscholar +1 more source
Revisiting high-order Taylor methods for astrodynamics and celestial mechanics [PDF]
Monthly notices of the Royal Astronomical Society, 2021 We present heyoka, a new, modern and general-purpose implementation of Taylor’s integration method for the numerical solution of ordinary differential equations.
F. Biscani, D. Izzo
semanticscholar +1 more source
The Spin–Spin Problem in Celestial Mechanics [PDF]
Journal of nonlinear science, 2021 We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortest physical axis and is perpendicular to the orbital plane.
A. Celletti +2 more
semanticscholar +1 more source
Parabolic orbits in Celestial Mechanics: a functional‐analytic approach
Proceedings of the London Mathematical Society, 2021 We prove the existence of half‐entire parabolic solutions, asymptotic to a prescribed central configuration, for the equation ẍ=∇U(x)+∇W(t,x),x∈Rd,where d⩾2 , U is a positive and positively homogeneous potential with homogeneity degree −α with α∈]0,2[ ,
A. Boscaggin +3 more
semanticscholar +1 more source
On stability of triangular points of the restricted relativistic elliptic three-body problem with triaxial and oblate primaries [PDF]
Serbian Astronomical Journal, 2017 This paper investigates the location and linear stability of triangular points under combined effects of perturbations: triaxialty of a massive primary, oblateness of a less massive one, and relativistic corrections. The primaries in this system
Zahra K. +3 more
doaj +1 more source
Analytical formulations to the method of variation of parameters in terms of universal Y's functions [PDF]
Serbian Astronomical Journal, 2015 The method of variation of parameters still has a great interest and wide applications in mathematics, physics and astrodynamics. In this paper, universal functions (the Y's functions) based on Goodyear's time transformation formula were used to
Sharaf M.A., Saad A.S., Selim H.H.
doaj +1 more source
Collision dynamics in Hénon-Heiles’ two-body problem [PDF]
Serbian Astronomical Journal, 2003 We tackle the two-body problem associated to Hénon-Heiles’ potential in the special case of the collision singularity. Using McGehee-type transformations of the second kind, we blow up the singularity and replace it by the collision manifold Mc pasted on
Mioc V., Barbosu M.
doaj +1 more source
The role of a steepness parameter in the exponential stability of a model problem: Numerical aspects [PDF]
Serbian Astronomical Journal, 2011 The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness.
Todorović N.
doaj +3 more sources