近地卫星轨道上方形薄板的超混沌  

Ultra-chaos of square thin plate in low Earth orbit

作　　者：张博 杨宇 廖世俊 Bo Zhang;Yu Yang;Shijun Liao(School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]不详

出　　处：《Acta Mechanica Sinica》2024年第5期175-183,共9页力学学报（英文版）

基　　金：This work was partly supported by the National Natural Science Foundation of China(Grant No.12272230);Shanghai Pilot Program for Basic Research-Shanghai Jiao Tong University(Grant No.21TQ1400202);the project"Development of Large-scale Spacecraft Flight and Reentry Surveillance and Prediction System"of Manned Space Engineering Technology(2018-2014)。

摘　　要：由于其小质量和偏心率,近地卫星轨道上的碎片运动可能是混沌的.本文所研究的在近地卫星轨道中偏质心的方形薄板是混沌的.混沌系统以其对初始条件的敏感依赖而闻名,但其统计特性通常对小扰动不敏感.然而,最近提出的一个名为超混沌的状态,其统计量对小扰动也同样敏感.本文表明,超混沌广泛存在于近地卫星轨道上的偏质心方形薄板中.结果显示,超混沌的轨迹比正常混沌的轨迹更为混乱,位置偏差可能比正常混沌大两个数量级.与以往发现的超混沌系统不同,本研究揭示了一个没有周期性边界的物理约束系统中的超混沌状态,而遗忘的超混沌系统至少有一个周期边界或缺乏物理边界.超混沌概念合理地解释了空间碎片可以扩散很大区域的原因,因为大多数碎片是偏质心的.Due to its small mass and eccentricity,the motion of a piece of debris in low Earth orbit(LEO)may be chaotic.This paper demonstrates that ultra-chaos widely exists in the case of a square thin plate in LEO with a center of mass(COM)that is initially displaced from the axis of symmetry.Chaotic systems are well-known for their sensitive dependence on initial conditions,though their statistical properties are usually insensitive to small disturbances.However,a recent concept called ultra-chaos has been introduced to describe chaotic systems whose statistics are sensitive to even tiny disturbances.This paper demonstrates that ultrachaos is widely exists in a square thin plate in LEO with a displaced COM from the axis of symmetry.The results show that an ultra-chaotic plate trajectory exhibits higher disorder than that of a normal plate,with a position deviation that can be two orders of magnitude larger than that of a normal-chaotic subsystem.Distinct from earlier findings concerning ultra-chaotic systems,the present study uncovers the manifestation of ultra-chaos in a physically constrained system devoid of periodic boundaries.Prior investigations of ultra-chaotic systems have featured at least one periodic boundary or lacked a physical boundary.The new concept of ultra chaos provides a plausible explanation as to why space debris can spread to a vast area,as most pieces of debris haveadisplaced COM.

关 键 词：超混沌 位置偏差 小扰动 物理约束 周期边界 混沌系统 物理边界 质心 

分 类 号：O311[理学—一般力学与力学基础]