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.