## 1 Introduction
[PERSON] [21] presented a set of Mathematica modules that organizes numerical integration rules considered useful for finite element work. [PERSON] et al. [3] developed a finite element scheme to solve the thermally induced bending-torsion coupling vibration of thin-walled beams and the thermal and structure coupling was taken into account. The aforementioned modeling methods provide the basis for solving the thermally induced coupled attitude and vibration problem. Generally, the thermally induced motion of satellite appendages consist of quasi-static deformation and superimposed vibration [4]. [PERSON] and [PERSON] [22] analyzed the flutter problem caused by the thermal impact of the solar panel when the satellite comes in and out of the shadowed area of the Earth. [PERSON] [23] conducted a thermal analysis of the hoop-truss antenna subjected to extreme heat load using the finite element method. [PERSON] [20; 24] analyzed flutter stable boundary for the thermoelastic-structure of spatial thin-walled beams under solar radiation. Through previous studies, it is found that thermal vibration has an important effect on the stability of the system, and this effect is exacerbated by the coupling motion of attitude and vibration. At this time, a control strategy is needed to ensure its stable operation [25]. Among all the control theories, the sliding mode control theory has received a good deal of attention because of its robustness and simplicity. In addition, the sliding mode control theory is suitable for such rigid-flexible systems with profound nonlinearity and modeling uncertainty. Successful applications to practical systems are numerous [25]. [PERSON] [26] designed the discontinuous attitude control law based on sliding mode control theory for adapting the unknown upper bounds of the lumped disturbance so that the limitation of knowing the bound of the disturbance in advance is released. [PERSON] [27] used adaptive sliding mode control with a mixed sliding surface to minimize the impact of uncertainty and interference. In order to stabilize the attitude of the flexible spacecraft, [PERSON] et al. [28] proposed a new adaptive fuzzy sliding mode control method to solve the time-delay dynamic model. [PERSON] and [PERSON] [29] used the sliding mode method to control the uniaxial attitude of the flexible spacecraft. Combining the positive position feedback controller and the piezoelectric actuator/sensor on the solar panel area, [PERSON] [30] used an adaptive sliding mode controller to adjust the attitude to suppress vibration. In conclusion, the coupled rigid-flexible model of spacecraft with irregular appendage can be established effectively based on the finite element model, and the thermally induced coupled dynamical behaviors and control strategy of the satellite's attitude motion and hoop-truss antenna's vibration under solar flux shock can be further studied, which is rarely mentioned in references. The paper is structured as follows. The rigid-flexible coupled dynamic model of spacecraft is derived by using the law of conservation of momentum and angular momentum in Section 2. In Section 3, an effective thermal-structural finite element model is developed to obtain the corresponding natural frequencies and modal shapes analytically. The results are validated by the comparisons with Multiphysics FEA. Finally, the dynamic behaviors of the satellite's attitude motion and hoop-truss antenna's vibration are investigated. Meanwhile, the attitude controller is designed using variable structure sliding mode control theory in Section 4. The conclusions are drawn in Section 5.