基于几何力学的类平板式卫星全耦合动力学

doi:10.7527/S1000-6893.2024.29786

Abstract

Abstract:

This paper focuses on the structural characteristics of plate-type satellites and establishes attitude-orbit-structure coupling dynamic equations in the Euler-Lagrange and Hamilton forms using Lagrange mechanics and Hamilton mechanics on the Lie group， respectively. This method simultaneously considers the coupling effect among the attitude， orbit， and plate structure appendage vibrations of spacecraft in orbit. The vibration phenomenon of the plate structure appendage is approximated by a single degree of freedom torsion spring model. This description method can easily describe the vibration phenomenon through Lie group tools. On the other hand， the dynamic equations derived from the perspectives of Lagrange geometry and Hamilton geometry are global and coordinate free. In addition， the establishment of the system dynamics model considers the time-varying characteristics of the satellite center of mass， making it more accurate. The effectiveness of this modeling method is verified using numerical examples. Through simulation comparison with the rigid model， the attitude-orbit-structure coupling effect of the quasi-plate satellite under excitation is analyzed. Results show that the model has good stability and can accurately predict the dynamic response of the quasi flat satellite in orbit under excitation.

Key words: plate-type satellite, Lagrange mechanics, Hamilton’s phase space variational principle, attitude-orbit-structure coupling, Lie group

CLC Number:

V412.4

Qian CAO, Huayi LI. Fully-coupled dynamics for plate-type satellite based on geometric mechanics[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(16): 229786-229786.

Figures/Tables 10

Fig.1

Table 1

Methods of classical mechanics

建模方法	形式
牛顿-欧拉力学	$F = m a τ = J ω ˙ + ω × J ω$
Lagrange力学	$∂ L ∂ q - d d t ∂ L ∂ q ˙ = 0$
Hamilton力学	$q ˙ = ∂ H ∂ p q, p p ˙ = - ∂ H ∂ q q, p$

Table 1

Fig.2

Fig.3

Table 2

Initial states

参数	数值
卫星初始位置	$r 0 = 6 971 00 T$ km
轨道倾角	56°
初始线速度	$v 0 = 0 4.228 5 6.269 0 T$ km/s
卫星初始姿态	$R 0 = I 3$
初始角速度	$ω 0 = 000 T$ rad/s
初始振动角速度	$θ ˙ 0 = 0$ rad/s
初始振动角位移	$θ 0 = 0$ rad

Table 2

Table 1

Simulation parameters

参数	数值
仿真时长	600 s
步长	0.1 s
整星质量	950 kg
中心刚体质量	850 kg
太阳翼质量	100 kg
板式附件安装姿态	$R H = - 1 00 0 c o s π 4 s i n π 4 0 - s i n π 4 c o s π 4$
中心刚体相对质心的转动惯量	$J h = d i a g 500,400,350$ kg·m²
太阳翼转动惯量（相对质心）	$J s a = d i a g 80,75,8$ kg·m²
中心刚体质心在体系下的位矢	$c B = 000 T$ m
太阳翼质心在 $Q$ 系下的位矢	$s = 1.5 00 T$ m
铰接点在体系下的位矢	$d = - 0.8 0.4 0.5 T$ m
刚度系数	$K y = 300 N ⋅ m / r a d$
阻尼系数	$C y = 0 N ⋅ m ⋅ s / r a d$

Table 1

Fig.4

Fig.5

Fig. 6

Fig.7

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Fully-coupled dynamics for plate-type satellite based on geometric mechanics

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