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首页> 外文会议>International Workshop on Computer Algebra in Scientific Computing(CASC 2006); 20060911-15; Chisinau(MD) >Numerical Study of Stability Domains of Hamiltonian Equation Solutions
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Numerical Study of Stability Domains of Hamiltonian Equation Solutions

机译：哈密​​顿方程解稳定性域的数值研究

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摘要

The computer algebra methods are effective means for the search of approximate and exact solutions of differential equations of theoretical physics, celestial mechanics, astrodynamics, and other natural sciences. Before appearance of Programming Systems such as Mathematica, Maple etc., we knew for classical Newtonian three-body problem only Euler exact collinear and Lagrange triangular solutions, for many-body problem - the rotating regular tetragon solution found by A. Dziobek and the general homographic solution theory developed by A. Winter in the 30es of the 20th century. An amount of similar research has grown recently due to the fact that the existence of central configurations of the many-body problem is eventually reduced to the solution of the systems of nonlinear algebraic-irrational equations, which can be solved only by the computer algebra methods, thanks to exceptional properties of them. We demonstrated that each of the exact particular solution of the Newtonian n—body problem differential equations generates a new dynamic model - the (n+1) restricted problem being a generalization of the noted Poincare-Jacobi model, the so-called restricted three-body problem. The latter is brought about by the well-known two-body problem.
机译：计算机代数方法是搜索理论物理学，天体力学，天体动力学和其他自然科学微分方程的近似和精确解的有效手段。在出现诸如Mathematica，Maple等编程系统之前，对于经典牛顿三体问题，我们只知道Euler精确共线解和Lagrange三角解，对于多体问题-A. Dziobek和一般人找到的旋转正则四边形解A. Winter在20世纪30年代提出的单应解理论。最近，由于多体问题的中心结构的存在最终被简化为非线性代数-无理方程组的解，因此只能通过计算机代数方法求解的事实已引起大量类似研究。 ，这要归功于它们的卓越性能。我们证明了牛顿n体问题微分方程的每个精确解都生成了一个新的动力学模型-（n + 1）受限问题是著名的Poincare-Jacobi模型的推广，即所谓的受限三项式身体问题。后者是由众所周知的两体问题引起的。

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