Results 11 to 20 of about 287 (170)
INTEGRABLE SYSTEMS IN SYMPLECTIC GEOMETRY [PDF]
Glasgow Mathematical Journal, 2007 AbstractQuaternionic vector mKDV equations are derived from the Cartan structure equation in the symmetric space=Sp(n+1)/Sp(1) ×Sp(n). The derivation of the soliton hierarchy utilizes a moving parallel frame and a Cartan connection 1-form ω related to the Cartan geometry onmodelled on$(\mk{sp}_{n+1}, \mk{sp}_{1}\,{\times}\, \mk{sp}_{n})$.
Asadi, E., Sanders, J.A.
openaire +3 more sources
A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS [PDF]
The Astronomical Journal, 2010 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 method is implemented in the parallel N-body code, PKDGRAV and tested on some simple orbits.
Quinn, T. +3 more
openaire +2 more sources
Symplectic groupoids for Poisson integrators
Journal of Geometry and Physics, 2023 We use local symplectic Lie groupoids to construct Poisson integrators for generic Poisson structures. More precisely, recursively obtained solutions of a Hamilton-Jacobi-like equation are interpreted as Lagrangian bisections in a neighborhood of the unit manifold, that, in turn, give Poisson integrators.
openaire +2 more sources
Anomaly in symplectic integrator [PDF]
Physics Letters A, 2007 6 pages, no ...
openaire +2 more sources
Universe, 2021 A small deformation to the Schwarzschild metric controlled by four free parameters could be referred to as a nonspinning black hole solution in alternative theories of gravity.
Hongxing Zhang +3 more
doaj +1 more source
Symplectic integrators for spin systems [PDF]
Physical Review E, 2014 We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in $\mathbb{R}^3$. Unlike splitting methods, it is defined for all Hamiltonians, and is $O(3)$-equivariant. It is a rare example of a generating function for symplectic maps of a noncanonical phase space. It yields an
Robert I. McLachlan +2 more
openaire +3 more sources
Symplectic integration of magnetic systems [PDF]
Journal of Computational Physics, 2014 Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the dynamics for an approximate Hamiltonian.
openaire +2 more sources
Universe, 2021 We mainly focus on the effects of small changes of parameters on the dynamics of charged particles around Kerr black holes surrounded by an external magnetic field, which can be considered as a tidal environment.
Xin Sun +5 more
doaj +1 more source
On the Nonlinear Stability of Symplectic Integrators [PDF]
BIT Numerical Mathematics, 2004 The paper deals mainly with the problem of achieving stability for symplectic numerical integrators by the mean of studying the topological equivalence of the level sets of the original Hamiltonian and those of the modified Hamiltonian associated to the numerical integrators.
Mclachlan, Robert Iain. +2 more
openaire +1 more source
Effects of Coupling Constants on Chaos of Charged Particles in the Einstein–Æther Theory
Universe, 2023 There are two free coupling parameters c13 and c14 in the Einstein–Æther metric describing a non-rotating black hole.
Caiyu Liu, Xin Wu
doaj +1 more source