基于参激共振的受摄小行星悬停轨道设计方法

司震; 钱霙婧; 杨晓东; 张伟

doi:10.6052/0459-1879-20-141

基于参激共振的受摄小行星悬停轨道设计方法

doi: 10.6052/0459-1879-20-141

北京工业大学材料与制造学部, 机械结构非线性振动与强度北京市重点实验室, 北京 100124

基金项目: 1) 国家自然科学基金面上项目(11772009)

详细信息

作者简介:
2) 钱霙婧, 副教授, 主要研究方向: 探测器轨道动力学、非线性动力学. E-mail: candiceqyj@163.com

通讯作者:
钱霙婧

中图分类号: V412.4⁺1,O313.1
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- 文章访问数: 2295
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- 被引次数: 0
出版历程
- 收稿日期: 2020-04-30
- 刊出日期: 2020-12-10

HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE

Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China

摘要

摘要: 本文将太阳引力摄动视为受摄不规则小行星系统的组成部分,借鉴非线性振动理论中参数激励共振的概念,创新性地设计了不规则小行星平衡点附近稳定的悬停观测轨道.为了同时考虑不规则小行星引力和太阳引力, 本文采用受摄粒杆模型描述系统.通过对未扰系统平衡点以及固有频率的分析, 给出系统存在参激共振轨道的条件.再以第二类参激主共振和1:3内共振为例,采用多尺度方法求得参数激励共振轨道的稳态解, 并对稳态解的稳定性进行判断.通过受摄小行星系统的幅频响应曲线以及力频响应曲线分析了系统的非线性特性以及参数激励效应.此外, 对内共振引起的长短周期能量转移现象进行了分析.本文的研究成果可以拓展现有小行星系统周期轨道族设计方法.
- 小行星 /
- 粒杆模型 /
- 悬停轨道 /
- 参数激励共振 /
- 非线性动力学
Abstract: In this paper, the solar gravitational perturbation is considered as a part of the asteroid system instead of treating it as perturbation. Based on the concept of parametric excitation resonance in nonlinear vibration theory, a novel stable parametric resonance orbit near the equilibrium point is designed. In order to consider the gravitational field of an irregular asteroid and the gravitational force of the Sun, the perturbed particle-linkage model is adopted. By analyzing the equilibrium points and the natural frequencies of the unperturbed system, the preconditions that the parametric resonance periodic orbit can exist are given. Taking the second principal resonance and 1:3 internal resonance as examples, the steady-state solutions of parametric resonance orbit are obtained by using multi-scale method. The stability of the steady-state solution is determined. The nonlinear dynamic behaviors of the system are analyzed by the amplitude-frequency response curve. In addition, parametric excitation effect caused by solar gravitational perturbation and the energy transfer phenomenon between long and short periodic motions are analyzed. The proposed method of this paper can expand the existing periodic orbit families near asteroids.
- asteroid /
- particle-linkage model /
- hovering orbit /
- parametric excitation resonance /
- nonlinear dynamic

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参考文献(1)

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