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Title: ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME

Abstract

We propose an accurate orbital integration scheme for the general three-body problem that retains all conserved quantities except angular momentum. The scheme is provided by an extension of the d'Alembert-type scheme for constrained autonomous Hamiltonian systems. Although the proposed scheme is merely second-order accurate, it can precisely reproduce some periodic, quasiperiodic, and escape orbits. The Levi-Civita transformation plays a role in designing the scheme.

Authors:
 [1]
  1. Tokushima Bunri University, Nishihama, Yamashiro-cho, Tokushima 770-8514 (Japan)
Publication Date:
OSTI Identifier:
22130903
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (New York, N.Y. Online); Journal Volume: 145; Journal Issue: 3; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANGULAR MOMENTUM; HAMILTONIANS; ORBITS; PERIODICITY; THREE-BODY PROBLEM; TRANSFORMATIONS

Citation Formats

Minesaki, Yukitaka. ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME. United States: N. p., 2013. Web. doi:10.1088/0004-6256/145/3/63.
Minesaki, Yukitaka. ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME. United States. doi:10.1088/0004-6256/145/3/63.
Minesaki, Yukitaka. 2013. "ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME". United States. doi:10.1088/0004-6256/145/3/63.
@article{osti_22130903,
title = {ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME},
author = {Minesaki, Yukitaka},
abstractNote = {We propose an accurate orbital integration scheme for the general three-body problem that retains all conserved quantities except angular momentum. The scheme is provided by an extension of the d'Alembert-type scheme for constrained autonomous Hamiltonian systems. Although the proposed scheme is merely second-order accurate, it can precisely reproduce some periodic, quasiperiodic, and escape orbits. The Levi-Civita transformation plays a role in designing the scheme.},
doi = {10.1088/0004-6256/145/3/63},
journal = {Astronomical Journal (New York, N.Y. Online)},
number = 3,
volume = 145,
place = {United States},
year = 2013,
month = 3
}