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Universal formulation for the N-body problem
Journal of Guidance, Control, and Dynamics, 1996Summary: The universal formulation for the perturbed two-body problem is generalized to cover all gravitational \(N\)-body problems involving a dominant central mass. Its efficiency, when compared to conventional numerical integration, is shown in several examples.
Zadunaisky, Pedro E. +1 more
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1996
The order of the chapters, and thus the framework of our treatment, reflects the fact that we have followed the traditional route; that is, to examine first the two-body problem and then the N-body problem. In abstract terms, it might appear more sensible to proceed backwards, from arbitrary N to the particular case N = 2.
Dino Boccaletti, Giuseppe Pucacco
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The order of the chapters, and thus the framework of our treatment, reflects the fact that we have followed the traditional route; that is, to examine first the two-body problem and then the N-body problem. In abstract terms, it might appear more sensible to proceed backwards, from arbitrary N to the particular case N = 2.
Dino Boccaletti, Giuseppe Pucacco
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1997
Suppose that two points (r 1, m 1) and (r 2, m 2) mutually interact with potential energy U(|r 1 − r 2|), so that the equations of motion have the form \({m_1}{\ddot r_1} = - \frac{{\partial U}}{{\partial {r_1}}},\;{m_2}{\ddot r_2} = - \frac{{\partial U}}{{\partial {r_2}}}.\)
V. I. Arnold +2 more
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Suppose that two points (r 1, m 1) and (r 2, m 2) mutually interact with potential energy U(|r 1 − r 2|), so that the equations of motion have the form \({m_1}{\ddot r_1} = - \frac{{\partial U}}{{\partial {r_1}}},\;{m_2}{\ddot r_2} = - \frac{{\partial U}}{{\partial {r_2}}}.\)
V. I. Arnold +2 more
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1974
Two years ago, in a lecture given at the Schladming Conference 1972, I reviewed the present status of the quantum mechanical three-body problem [1]. It was the main intention of this survey to illustrate the way in which the properties of the integral equations, studied in this field, are related to basic concepts of multichannel collision theory. Such
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Two years ago, in a lecture given at the Schladming Conference 1972, I reviewed the present status of the quantum mechanical three-body problem [1]. It was the main intention of this survey to illustrate the way in which the properties of the integral equations, studied in this field, are related to basic concepts of multichannel collision theory. Such
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The Integral Manifolds of the N Body Problem
Journal of Dynamics and Differential Equations, 2021The \(N\)-\textit{body problem} refers to the study of the dynamics of a system of \(N\) point masses, moving under their mutual gravitational attraction. For such a system, it is a classical fact that there are conserved quantities of center of mass, linear momentum, angular momentum and energy.
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2016
When going from two bodies to three, or more, bodies, the complexity increases significantly, due to their mutual attractions. The two-body problem can be mathematically formulated so a closed-form solution is possible. With more than two bodies, it is impossible to formulate such a solution. There are some special cases, however, that can be handled.
Pini Gurfil, P. Kenneth Seidelmann
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When going from two bodies to three, or more, bodies, the complexity increases significantly, due to their mutual attractions. The two-body problem can be mathematically formulated so a closed-form solution is possible. With more than two bodies, it is impossible to formulate such a solution. There are some special cases, however, that can be handled.
Pini Gurfil, P. Kenneth Seidelmann
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The global solution of the N-body problem
CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Towards an Adaptive Treecode for N-body Problems
Journal of Scientific Computing, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benjamin W. Ong, Satyen Dhamankar
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On the global solution of the N-body problem
Celestial Mechanics & Dynamical Astronomy, 1993In connection with the publication of \textit{Wang Qiu-Dong} [Celestial Mech. Dyn. Astron. 50, No. 1, 73-88 (1991; Zbl 0726.70006)] the Poincaré type methods of obtaining the maximal solution of differential equations are discussed. In particular, it is shown that the Wang Qiu- Dong's global solution of the \(N\)-body problem has been obtained in the ...
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Evolving trajectories of the N-body problem
2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), 2008The N-body problem in k dimensions is the task of determining the time evolution of a system of kN second order ordinary differential equations according to Newtonpsilas inverse square law. It comes up in astrophysics as an approximation to celestial systems.
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