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Применение симплектических методов численного интегрирования для моделирования эволюции Плутона и астероида Хирон

Transactions of IAA RAS, issue 4, 330–341 (1999)

Keywords: радиоинтерферометрия со сверхдлинными базами (РСДБ), астрометрия, геодинамика, небесная механика, симплектические методы интегрирования гамильтоновых систем, плоская круговая ограниченная задача 3-х тел, симплектический интегратор для задачи n-тел

Abstract

Symplectic methods of Hamiltonian systems numerical integration are considered. Symplectic methods conserve symplectic structure of systems. They are reliable for integration in large intervals of time. Nonsymplectic methods of numerical integration bring the nonconservative effects in the considered system. The explicit schemes of symplectic integrators developed by Ruth, Forest, Neri, Yoshida. The construction of symplectic methods based on Lie algebras theory. The fields of possible application of the symplectic methods for celestial mechanics problems are considered. In this work for restricted circular tree-body problem in Jacobi coordinates symplectic integrator was constructed. The comparison of integration results of plane circular restricted tree-body problem for asteroid Juno obtained by Runge-Kutta methods and symplectic one is made. For n-body problem Yoshida's symplectic integrator was constructed. The pictures of evolution of Pluto and asteroid Chiron are obtained by this symplectic integrator.

Citation

Text

BibTeX

RIS

N. A. Sushko. Применение симплектических методов численного интегрирования для моделирования эволюции Плутона и астероида Хирон // Transactions of IAA RAS. — 1999. — Issue 4. — P. 330–341.

@article{sushko1999,
  abstract = {Symplectic methods of Hamiltonian systems numerical integration are considered. Symplectic methods conserve symplectic structure of systems. They are reliable for integration in large intervals of time.  Nonsymplectic methods of numerical integration bring the nonconservative effects in the considered system. The explicit schemes of symplectic integrators developed by Ruth, Forest, Neri, Yoshida.  The construction of symplectic methods based on Lie algebras theory.  The fields of possible  application of the symplectic methods for celestial mechanics problems are considered. In this work for restricted circular tree-body problem in Jacobi coordinates  symplectic integrator was constructed. The comparison of integration results of plane circular restricted tree-body problem for asteroid Juno obtained by Runge-Kutta methods and symplectic one is made. For n-body problem Yoshida's symplectic integrator was constructed. The pictures of evolution of Pluto and asteroid Chiron are obtained by this symplectic integrator.},
  author = {N.~A. Sushko},
  issue = {4},
  journal = {Transactions of IAA RAS},
  keyword = {радиоинтерферометрия со сверхдлинными базами (РСДБ), астрометрия, геодинамика, небесная механика, симплектические методы интегрирования гамильтоновых систем, плоская круговая ограниченная задача 3-х тел, симплектический интегратор для задачи n-тел},
  note = {russian},
  pages = {330--341},
  title = {Применение симплектических методов численного интегрирования для моделирования эволюции Плутона и астероида Хирон},
  url = {http://iaaras.ru/en/library/paper/249/},
  year = {1999}
}

TY  - JOUR
TI  - Применение симплектических методов численного интегрирования для моделирования эволюции Плутона и астероида Хирон
AU  - Sushko, N. A.
PY  - 1999
T2  - Transactions of IAA RAS
IS  - 4
SP  - 330
AB  - Symplectic methods of Hamiltonian systems numerical integration are
considered. Symplectic methods conserve symplectic structure of
systems. They are reliable for integration in large intervals of
time.  Nonsymplectic methods of numerical integration bring the
nonconservative effects in the considered system. The explicit
schemes of symplectic integrators developed by Ruth, Forest, Neri,
Yoshida.  The construction of symplectic methods based on Lie
algebras theory.  The fields of possible  application of the
symplectic methods for celestial mechanics problems are considered.
In this work for restricted circular tree-body problem in Jacobi
coordinates  symplectic integrator was constructed. The comparison of
integration results of plane circular restricted tree-body problem
for asteroid Juno obtained by Runge-Kutta methods and symplectic one
is made. For n-body problem Yoshida's symplectic integrator was
constructed. The pictures of evolution of Pluto and asteroid Chiron
are obtained by this symplectic integrator.
UR  - http://iaaras.ru/en/library/paper/249/
ER  -