## 1 Introduction
Additionally, the harmonic superposition form of fixed frequency and amplitude is used as input, and the different characteristics of disturbance source output under different flywheel rotation speeds are not considered. [PERSON] et al. used the Rosenblueth method and Fourier transform to transform the data between time-domain and frequency-domain and proposed a calculation method to convert frequency-domain image shift into a modulation transfer function (MTF) [16; 17; 18]. This method theoretically verified the influence of micro-vibration on imaging indicators, and it more conveniently reflected the influence of micro-vibration on imaging quality, but it did not consider the impact of the control subsystem. [PERSON] et al. analyzed the causes of flywheel disturbances in detail from two aspects of structural disturbance and harmonic disturbance; the mechanical model for each disturbance is established corresponding to its characteristics. A flywheel disturbance test platform is established based on the Kistler table system. Two different types of flywheels are tested, and the dynamic characteristics of the flywheel disturbances are analyzed [19; 20]. [PERSON] et al. researched the influence of flywheel disturbance on time-delayed and integration charge-coupled device (TDICCD) camera and satellite platform, which mainly includes two aspects: directly causing image shift and directly causing the jitter of a satellite platform. The influence of platform micro vibration on the image motion of an optical load is discussed from three aspects: the principle of the TDICCD camera, the classification of image motion, and the mechanism of image motion change caused by micro-vibration [21; 22]. [PERSON] et al. introduced a nonlinear dynamics model for these micro-vibrations with five degrees of freedom. The main advantage of the proposed model is that it analytically considers various disturbance sources [23]. [PERSON] et al. presented a first-principles-based derivation of the motion equations for a spacecraft with react wheels subject to general static and dynamic imbalances. The resulting formulation retains the true physics governing this fully coupled jitter phenomenon. As a result, energy and momentum checks are available by using this model [24]. [PERSON] et al. investigated the coupled micro-vibration dynamics of a cantilever configured reaction wheel assembly mounted on either a stiff or flexible platform [25]. Compared with the disadvantages in the previous literature, we have improved the integrated modeling method. Based on a high-resolution optical remote sensing satellite, this paper proposes an integrated modeling method for flywheel micro-vibration problems. The novelty or contribution of this paper are as follows:  
1. The model fully considers the variable speed operation of flywheels caused by a control subsystem during the imaging process in orbit, and it realizes the coupling and integration of vibration source, structure, control, and optical subsystem with a high degree of realism and accuracy. A comparison of simulation results and experimental results shows that the frequency errors at typical responses are all less than 0.4%; although the amplitude errors at typical responses are larger, the mean root square error is less than 35%. It can be considered that the proposed simulation model can accurately predict the impacts of micro-vibration of flywheels in orbit;
2. A new form of micro-vibration cosine harmonic superposition vibration source model is established, which not only satisfies the simulation of the overall model in the time-domain, but also considers the fact that a flywheel has different micro-vibration disturbance characteristics due to different flywheel rotation speed; the proposed model in this paper takes imaging mission instructions as input, and the vibration source subsystem is completely closed-loop within the overall frame;
3.