HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE 1)

doi:10.6052/0459-1879-20-141

Abstract

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.

Key words: asteroid, particle-linkage model, hovering orbit, parametric excitation resonance, nonlinear dynamic

CLC Number:

Si Zhen, Qian Yingjing, Yang Xiaodong, Zhang Wei. HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE ¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1774-1788.

Figures/Tables 9

Fig. 1 Perturbed particle-linkage model

Fig. 2 Distributions of equilibrium points with variations of parameters

Fig. 3 Parametric resonance region when $\sigma $ = 0.8, $k$ = 0.9

Fig. 4 Parametric resonance regions with different $k$ and $\sigma $

Fig. 5 Frequency-amplitude response curves (Case 1, Case 3)

Fig. 6 Frequency-amplitude response curves (Case 2, Case 4)

Fig. 7 Amplitude of the excitation-amplitude of response curves

Fig. 8 Stable parametric resonance orbit when $\sigma =0.8$, $k=0.9$, $\mu =0.001 13$, $\beta=0.014$

Fig. 9 Stable parametric resonance orbit when $\sigma =0.8$, $k=0.9$,$\mu =0.001$, $\beta =0.012$

References 40

[1]	柳森, 党雷宁, 赵君尧等. 小行星撞击地球的超高速问题. 力学学报, 2018,50(6):1311-1327
	( Liu Sen, Dang Leining, Zhao Junyao, et al. Hypervelocity issues of Earth impact by asteroids. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(6):1311-1327 (in Chinese))
[2]	Fujiwara A, Kawaguchi J, Yeomans DK, et al. The rubble-pile asteroid itokawa as observed by Hayabusa. Science, 2006,312(5778):1330-1334 DOI URL PMID
[3]	Muller T, Durech J, Ishiguro M, et al. Hayabusa-2 Mission Target Asteroid 162173 Ryugu (1999 JU3): Searching for the object's spin-axis orientation. Astronomy & Astrophysics, 2017,599:A103
[4]	Lauretta DS, Balram-knutson SS, Beshore E, et al. OSIRIS-REx: Sample Return from Asteroid (101955) Bennu. Space Science Reviews, 2017,212(1-2):925-984 DOI URL
[5]	崔平远, 乔栋. 小天体附近轨道动力学与控制研究现状与展望. 力学进展, 2013,43(5):526-539 DOI URL
	( Cui Pingyuan, Qiao Dong. State-of-the-art and prospects for orbital dynamics and control near small celestial bodies. Advances in Mechanics, 2013,43(5):526-539 (in Chinese)) DOI URL
[6]	曾祥远, 李俊峰, 刘向东. 细长小行星探测动力学与控制. 北京: 清华大学出版社, 2019
	( Zeng Xiangyuan, Li Junfeng, Liu Xiangdong. Dynamics and Control over Elongated Asteroids. Beijing: Tsinghua University Press, 2019 (in Chinese))
[7]	Nardi L, Palomba E, Longobardo A, et al. Mapping olivine abundance on asteroid (25143) Itokawa from Hayabusa_NIRS data. Icarus, 2019,14:321-349
[8]	Scheeres DJ. Close proximity dynamics and control about asteroids// Proceedings of the American Control Conference. Portland, OR: American Control Conference, 2014: 1584-1598.
[9]	Broschart SB, Scheeres DJ. Control of hovering spacecraft near small bodies: Application to Asteroid 25143 Itokawa. Journal of Guidance Control and Dynamics, 2005,28(2):343-354
[10]	孙加亮, 田强, 胡海岩. 多柔体系统动力学建模与优化研究进展. 力学学报, 2019,51(6):1565-1586
	( Sun Jialiang, Tian Qiang, Hu Haiyan. Advances in dynamic modeling and optimization of flexible multibody systems. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1565-1586 (in Chinese))
[11]	曹登庆, 白坤朝, 丁虎等. 大型柔性航天器动力学与振动控制研究进展. 力学学报, 2019,51(1):1-13
	( Cao Dengqing, Bai Kunchao, Ding Hu, et al. Advances in dynamics and vibration control of large-scale flexible spacecraft. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(1):1-13 (in Chinese))
[12]	Scheeres DJ. Stability of hovering orbits around small bodies// 9th Annual Space Flight Mechanics Meeting. Breckenridge, CO: Advances in the Astronautical Sciences, 1999, 1-2:855-873
[13]	Sawai S, Scheeres DJ, Broschart SB. Control of hovering spacecraft using altimetry. Journal of Guidance Control and Dynamics, 2002,25(4):786-795
[14]	Sawai S, Scheeres DJ. Hovering and translational motions over small bodies. Advances in the Astronautical Sciences, 2001,108:781-796
[15]	Broschart SB, Scheeres DJ. Boundedness of spacecraft hovering under dead-band control in time-invariant systems. Journal of Guidance Control and Dynamics, 2007,30(2):601-610
[16]	Zhang P, Ma TH, Zhao B, et al. Robust linear quadratic regulator via sliding mode guidance for spacecraft orbiting a tumbling asteroid. Mathematical Problems in Engineering, 2015,2015(Pt.21):947843
[17]	Zeng XY, Gong SP, Li JF, et al. Solar sail body-fixed hovering over elongated asteroids. Journal of Guidance, Control, and Dynamics, 2016,39(6):1223-1231 DOI URL
[18]	Daniel C, Alexis P, Anne L. Long-term evolution of space debris under the J2 effect, the solar radiation pressure and the solar and lunar perturbations. Celestial Mechanics and Dynamical Astronomy volume, 2015,123(2):223-238
[19]	Zhao CY, Zhang MJ, Wang HB, et al. Two-dimensional phase plane structure and the stability of the orbital motion for space debris in the geosynchronous ring. Advances in Space Research, 2013,52(4):677-684 DOI URL
[20]	Hamilton DP, Burns JA. Orbital stability zones about asteroids: II. The destabilizing effects of eccentric orbits and of solar radiation. Icarus, 1992,96(1):43-64 DOI URL
[21]	Heiligers J, Scheeres DJ. Solar-sail orbital motion about asteroids and binary asteroid systems. Journal of Guidance, Control, and Dynamics, 2018,41(9):1947-1962 DOI URL
[22]	Morrow E, Scheeres DJ, Lubin D. Solar sail orbit operations at asteroids. Journal of Spacecraft and Rockets, 2001,38(2):279-286 DOI URL
[23]	Williams T, Abate M. Capabilities of furlable solar sails for asteroid proximity operations. Journal of Spacecraft and Rockets, 2009,46(5):967-975 DOI URL
[24]	Giancotti M, Funase R. Solar sail equilibrium positions and transfer trajectories close to a trojan asteroid// The 63rd International Astronautical Congress, 2012
[25]	Feng JL, Hou XY. Secular dynamics around small bodies with solar radiation pressure. Communications in Nonlinear Science and Numerical Simulation, 2019,76, 71-91 DOI URL
[26]	Xin XS, Scheeres DJ, Hou XY. Forced periodic motions by solar radiation pressure around uniformly rotating asteroids. Celestial Mechanics and Dynamical Astronomy, 2016,126(4):405-432 DOI URL
[27]	辛晓生. 小行星探测器轨道动力学. [博士论文]. 南京: 南京大学, 2017: 89-108
	( Xin Xiaosheng. Orbital dynamics about asteroids. [PhD Thesis]. Nanjing: Nanjing University, 2017: 89-108 (in Chinese))
[28]	刘莹莹, 刘睿, 周军. 摄动力对绕飞小行星航天器轨道的影响. 飞行力学, 2008,26(3):44-48
	( Liu Yingying, Liu Rui, Zhou Jun. Research on orbit of spacecraft circling planetoid influenced by dragging force. Flight Dynamics, 2008,26(3):44-48 (in Chinese))
[29]	倪彦硕, 宝音贺西, 李俊峰. 考虑太阳摄动的小行星附近轨道动力学. 深空探测学报, 2014,1(1):67-74
	( Ni Yanshuo, Baoyin Hexi, Li Junfeng. Orbit dynamics in the vicinity of asteroids with solar perturbation. Journal of Deep Space Exploration, 2014,1(1):67-74 (in Chinese))
[30]	Qian YJ, Yang LY, Yang XD, et al. Parametric stability analysis for planar bicircular restricted four-body problem. Astrodynamics, 2018,2:147-159 DOI URL
[31]	Qian YJ, Yang XD, Wu H, et al. Gyroscopic modes decoupling method in parametric instability analysis of gyroscopic systems. Acta Mechanica Sinica, 2018,222(2):963-969
[32]	司震, 钱霙婧, 杨晓东等. 基于扰动粒杆模型的强不规则小行星的参激稳定分析// 北京力学会第二十五届学术年会会议论文集. 2019: 827-828
	( Si Zhen, Qian Yingjing, Yang Xiaodong, et al. Parametric stability analysis for irregular-shaped asteroids based on perturbed particle-linkage model// Proceedings of the 25th Annual Conference of Beijing Society of Theoretical and Applied mechanics. 2019: 827-828 (in Chinese))
[33]	Lei Hanlun, Circi C, Ortore E. Secular dynamics around uniformly rotating asteroids. Monthly Notices of the Royal Astronomical Society, 2019,485(2):2731-2743 DOI URL
[34]	Nayfeh AH, Mook DT. Nonlinear Oscillations. New York: Clarendon, 1979: 384-390
[35]	李晓玉, 岳宝增. 基于多尺度方法的平动圆柱贮箱航天器刚-液耦合动力学研究. 力学学报, 2019,51(5):1448-1454
	( Li Xiaoyu, Yue Baozeng. Study on the rigid-liquid coupling dynamics of a cylindrical-tank spacecraft in translation based on muti-scale method, Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1448-1454 (in Chinese))
[36]	Yang HW, Li S, Xu C. A particle-linkage model for non-axisymmetric elongated asteroids. Research in Astronomy and Astrophysics, 2018,18(7):84 DOI URL
[37]	Zeng XY, Jiang FH, Li JF, et al. Study on the connection between the rotating mass dipole and natural elongated bodies. Astrophysics and Space Science, 2015,356(1):29-42 DOI URL
[38]	Lan L, Yang HW, Baoyin HX, et al. Retrograde near-circular periodic orbits near equatorial planes of small irregular bodies. Astrophysics & Space Science, 2017,362(9):169-182
[39]	Zeng XY, Zhang YL, Yu Y, et al. The dipole segment model for axisymmetrical elongated asteroids. Astronomical Journal, 2018,155(2):85-102 DOI URL
[40]	Lei HL, Xu B. Analytical study on the motions around equilibrium points of restricted four-body problem. Communications in Nonlinear Science and Numerical Simulation, 2015,29(1-3):441-458 DOI URL

HOVERING ORBITS DESIGN FOR PERTURBED ASTEROIDS WITH PARAMETRIC EXCITATION RESONANCE ¹⁾

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