The Noether’s theorem is one of footstones in modern physics and mechanics, due to the correlations it has established between the conservation laws and the symmetries. The origin, the content and the related anecdotes of the Noether’s theorem are reviewed, as well as the relations between the J-integral, the Eshelby tensor and the Noether’s theorem.

Leonardo da Vinci, known as painter, sculptor, astronomer, inventor, musician, mathematician,anatomist, physiologist, geologist, botanist, writer, military engineer, architect and cartographer, is a representative figure of the Italian Renaissance humanism. This paper describes another aspect of Da Vinci：his research results of fluid mechanics and the contributions related with turbulence, flight, wave and storm, and it is concluded that he is the pioneer and founder of fluid mechanics science as well.

In this paper, the paper folding problem is simplified to a three-point bending model of a simply supported beam with a rectangular cross section under the concentrated force acting on the middle position. The maximal folding times of a sheet of A4 printing paper and octavo newspaper under a normal human force are related with the maximum bending deflections and the minimum folding loads. The results show that for an ordinary A4 printing paper, an adult can only fold 6 times, or up to 7 times under extreme circumstances. For an octavo newspaper, an adult can easily fold 7 times, but not 8 times. The test results are in good agreement with the theoretical predictions.

In the appreciation of the ancient poem for dragonflies, we discuss the magical hydrodynamic characteristics of dragonflies, which have evolved for hundreds of millions of years. The dragonfly's compound eye, the wings' ability of eliminating chatter, the superhydrophobicity of its epidermis, the drag reduction by its scales, and the mechanical characteristics of the water-jet propulsion of the dragonfly larvae; and their inspiration to the development of engineering technology are discussed. At the same time, the development status of the dragonfly robots is introduced as well.

The China Trajectory Optimization Competition (CTOCorganized by The Chinese Society of Theoretical and Applied Mechanics, has been successfully held for ten years since its initiation in 2009. With unremitting efforts during the past ten years, CTOC has become a communication platform for domestic universities and research institutions on space trajectory design and optimization research. It not only identifies research talents for space exploration, but also provides knowledge and ideas for this field. This article reviews the development history and achievements of CTOC following the timeline from 2009 to 2019, and summarizes the main features and innovations of the competition.

The 10th Global Trajectory Optimisation Competition hosted by Jet Propulsion Laboratory (JPL) came to an end in June 2019, and the Chinese team won the championship for the first time. For the first time in history, this competition is based on the sci-fi mission, designing the optimal orbit to settle in 100000 Milky Way stars. This paper introduces the tasks, gravity model and spacecraft maneuver model of the Galaxy settlement mission, and analyzes the merit function of this competition specifically. The tree structure is introduced to represent the settlement solution, and the design method of the initial settler distribution is described. Simultaneously, the forward and reverse tree generation strategies are introduced and compared. The methods of local optimization and topology reconstruction of settlement trees used in the competition are briefly introduced. In the galaxy-s stars map, the champion solution was presented in tree structures. The significance of this competition was summarized and some useful inspirations were obtained.

This paper discusses the science fiction film "The Wandering Earth" from the point of view of mechanics, and the possibility of the future technology imagined in this film is discussed.

The essence of Sonic-Boom-Cloud is the water vapour condensation cloud caused by the local acceleration and the temperature decreased to the dew point and below, as the flying aircraft passes the high humidity air. It is more appropriate to call it the Condensation Cloud instead of the Sonic-Boom-Cloud. According to the flight speed and their different features, the Condensation Clouds can be divided into three types: the Low Subsonic Speed Irregular Condensation Cloud, the High Subsonic Speed Cone Condensation Cloud and the Supersonic Speed Cone Condensation Cloud. The formation mechanisms of the three types of Condensation Clouds, their different features, their relationship with the shock wave and the Sonic-Boom are discussed in this paper. The first type has no relationship with the Sonic-Boom. The second type is accompanied by the local weak shock wave, it does not break through the Sound Barrier and it is basically irrelevant with the Sonic Boom. The third type is related with the supersonic shock wave and the Sonic Boom.

To enhance the students' interest for studying Theoretical Mechanics, two teaching cases of static equilibrium are designed in this paper, as the static analysis for birds standing on a branch. Some knowledge points, such as the parallelogram of force, the transmissibility of force, the three-force balance intersecting principle and the conditions of rigid body equilibrium, are used to analyze the forces on the bird' legs on a branch; and the function of the woodpecker tail when it pecked the worm. It is a very enjoyable and educational experience for the students, and can raise students' interest in learning and improve teaching results.