具有相互作用的N粒子系统模型的平稳轨迹构造
Construction of stationary trajectories for a model of a system of N particles with interaction
AI总结：
针对经典N体问题，提出通过物理意义明确的数学规划优化求特征量条件最小值的方法，可构造平面平稳与周期轨迹，且三维空间中满足尺寸最小条件的轨迹必为平面轨迹。
摘要：
针对经典N体问题，本文提出一种方法，其核心是引入若干具有物理意义的自然数学规划优化问题，用于在系统可能状态集合上求解系统特征量的条件最小值。这些问题的解随后可用于构造系统的平面平稳轨迹族和周期轨迹族，还能推导这些轨迹上系统特征量之间的关系与估计值。研究表明，当系统在平面上沿由这些优化问题的全局最小值生成的轨迹运动时，在任意时刻，系统的“内聚性”（或势能）处于当前水平下，系统的尺寸都会达到最小可能值。本文还研究了三维空间中用于求解系统特征量条件最小值的类似优化问题。结果显示，这些问题的解只能在系统的平面轨迹上取得，尤其能在构造出的平面平稳轨迹和周期轨迹上取得。此外，研究还证明，若三维空间中系统的某条轨迹至少存在一个点，使得系统在当前内聚性（或势能）取值下达到最小可能尺寸，则该轨迹只能是平面轨迹；而这类轨迹具体包括由所研究的优化问题的全局最小值生成的平面平稳轨迹和周期轨迹。
英文摘要：
For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the system on the set of its possible states. The solution of these problems then makes it possible to construct families of flat stationary and periodic trajectories of the system and also to find relationships and estimates for the characteristics of the system on these trajectories. It is shown that when the system moves on a plane on trajectories generated by the global minimum in these optimization problems, at any time the minimum possible size of the system is achieved at each current level of its "cohesion" (or potential energy). Similar optimization problems are considered for finding a conditional minimum for the characteristics of a system in three-dimensional space. It is shown that the solution of these problems can be achieved only on flat trajectories of the system and is achieved, in particular, on the constructed flat stationary and periodic trajectories. In addition, it is shown that the trajectory of the system in three-dimensional space, at least at one point of which the minimum possible size of the system is achieved at the current value of its cohesion (or potential energy), can only be flat. And such trajectories are, in particular, flat stationary and periodic trajectories generated by the global minimum in the considered optimization problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
