## 1 Introduction  
Small spacecraft are playing an increasingly important role in space missions [1; 2; 3]. Despite their small size, they are modern complex technical systems. However, it is necessary to conduct additional research to use them effectively. This is primarily due to the fact that the mass fraction of flexible elements in the total mass of the small spacecraft is higher than that of other space technology [4; 5]. This situation is explained by the requirements for the electricity generated by solar panels, which is necessary for the effective functioning of the target equipment of the small spacecraft [6; 7]. Some small spacecraft do not have flexible solar panels and are used in uncontrolled motion [7; 8; 9; 10]. The controlled motion of small spacecraft has a number of features due to the more significant influence of flexible elements on this motion [11; 12; 13]. Therefore, in addition to the traditional disturbances from solar panels associated with their natural oscillations, it is necessary to take into account other factors [14; 15; 16]. One of these factors is the temperature shock [17; 18; 19; 20; 21]. Temperature shock occurs when the spacecraft enters the Earth's shadow and exits it during its orbital motion. According to the research carried out in [22], it has a significant effect only on small spacecraft motion. Therefore, it is necessary to take it into account when performing individual target tasks. Examples of such tasks are remote sensing of the Earth from space [23; 24; 25] or implementation of gravity-sensitive technological processes on board small spacecraft [26; 27; 28]. Thus, it is necessary to meet the orientation requirements for remote sensing of the Earth [29; 30; 31]. These requirements are becoming increasingly high over time due to the increase in remote sensing resolution [32; 33]. In many works, for example [34; 35], the authors indicate that temperature shock can violate the orientation requirements. This is especially true of the requirements for the angular velocity of the small spacecraft rotation at the time of remote sensing of the Earth [36; 37]. An even more complicated situation arises when gravity-sensitive processes are implemented on board the spacecraft. They impose high requirements on the level of micro-accelerations in the working area of technological equipment [38; 39; 40]. Studies [41; 42; 43] show that temperature shock can significantly violate these requirements. Therefore, for the effective use of small spacecraft in the field of space technologies, it is necessary not only to study and evaluate the temperature shock effect but also to develop algorithms to neutralize this influence using the executive bodies of the orientation and motion control system of the small spacecraft [44]. Considering the prospects for the development of space technology, then the use of new types of solar panels, for example, ROSA [45; 46; 47], poses the problem of temperature shock more widely than is done in this review. Experiments on the International Space Station with ROSA solar panels have shown that the problem of small spacecraft controllability becomes acute when using them. The use of ROSA panels is extremely promising for small spacecraft due to the reduced weight of the structure when using them. However, the controllability of the spacecraft is also significantly reduced due to thermal fluctuations [19; 23] caused by temperature shock. Reference [44] presents an algorithm for linear and piecewise linear control of the small spacecraft to neutralize temperature shock. Reference [22] presents an analysis of the disturbing factors significant in temperature shock. Both of these works are devoted to the research of a small spacecraft with one flexible element. An example of such a spacecraft is Earth Observing One (EO-1) [48]. However, small spacecraft with an even number of flexible elements are more common. For example, the Aist-2D small Earth remote sensing spacecraft has two flexible elements in the form of solar panels [24; 49].