Inclusion of Non-Conservative Forces in Geometric Integrators with Application to Orbit–Attitude Coupling

2021 ◽  
pp. 1-14
Author(s):  
Dante A. Bolatti ◽  
Anton H. J. de Ruiter
Keyword(s):  
Geometric Integrators

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

scholarly journals Geometric Integrators for Classical Spin Systems

1997 ◽  
Vol 133 (1) ◽  
pp. 160-172 ◽  
Author(s):  
Jason Frank ◽  
Weizhang Huang ◽  
Benedict Leimkuhler
Keyword(s):  
Spin Systems ◽  
Classical Spin ◽  
Geometric Integrators

scholarly journals A review of some geometric integrators

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Dina Razafindralandy ◽  
Aziz Hamdouni ◽  
Marx Chhay
Keyword(s):  
Geometric Integrators

scholarly journals High-order geometric integrators for representation-free Ehrenfest dynamics

2021 ◽  
Vol 155 (12) ◽  
pp. 124104
Author(s):  
Seonghoon Choi ◽  
Jiří Vaníček
Keyword(s):  
High Order ◽  
Geometric Integrators

Geometric Integrators and Computing Ergodic Limits

2021 ◽  
pp. 313-420
Author(s):  
Grigori N. Milstein ◽  
Michael V. Tretyakov
Keyword(s):  
Geometric Integrators

An implementation of geometric integration within Matlab

SIMULATION ◽  
2019 ◽  
Vol 95 (11) ◽  
pp. 1055-1067
Author(s):  
Guillaume Chauvon ◽  
Philippe Saucez ◽  
Alain Vande Wouwer
Keyword(s):  
Kepler Problem ◽  
Size Composition ◽  
Variable Step Size ◽  
Step Size ◽  
System Variable ◽  
Geometric Integrators ◽  
Long Run ◽  
Variable Step ◽  
Long Time ◽  
Better Than

Geometric integrators allow preservation of specific geometric properties of the exact flow of differential equation systems, such as energy, phase-space volume, and time-reversal symmetry, and are particularly reliable for long-run integration. In this study, variable step size composition methods and Gauss methods are implemented in Matlab library integrators, and are tested with several representative problems, including the Kepler problem, the outer solar system and a conservative Lotka–Volterra system. Variable step size integrators often perform better than their fixed step size counterparts and the numerical results show excellent long time preservation of the Hamiltonian in these examples.

scholarly journals HIGHER-ORDER GEOMETRIC INTEGRATORS FOR A CLASS OF HAMILTONIAN SYSTEMS

2013 ◽  
Vol 11 (01) ◽  
pp. 1450009 ◽  
Author(s):  
ASIF MUSHTAQ ◽  
ANNE KVÆRNØ ◽  
KÅRE OLAUSSEN
Keyword(s):  
Angular Momentum ◽  
Differential Equations ◽  
Conservation Laws ◽  
Large Class ◽  
Hamiltonian Systems ◽  
Symplectic Geometry ◽  
Hamiltonian Mechanics ◽  
Rotation Invariant ◽  
Geometric Integrators ◽  
Kinetic And Potential Energies

We discuss systematic extensions of the standard (Störmer–Verlet) method for integrating the differential equations of Hamiltonian mechanics. Our extensions preserve the symplectic geometry exactly, as well as all Nöether conservation laws caused by joint symmetries of the kinetic and potential energies (like angular momentum in rotation invariant systems). These extensions increase the accuracy of the integrator, which for the Störmer–Verlet method is of order τ2 for a timestep of length τ, to higher-orders in τ. The schemes presented have, in contrast to most previous proposals, all intermediate timesteps real and positive. The schemes increase the relative accuracy to order τN (for N = 4, 6 and 8) for a large class of Hamiltonian systems.

Structure of B-series for Some Classes of Geometric Integrators

2009 ◽  
Author(s):  
Elena Celledoni ◽  
Robert I. McLachlan ◽  
Brynjulf Owren ◽  
G. R. W. Quispel ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Geometric Integrators
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