Dynamic symmetries

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  • Tham khảo sách 'spt 2001 symmetry and perturbation theory', khoa học tự nhiên, toán học phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • The International Symposium on Nuclear Structure Physics (NP2001) was held in Gottingen Germany, March 5-8, 2001. The aim of the Symposium was to discuss recent achievements and new initiatives for research in nuclear structure and to celebrate the career of Peter von Brentano.

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  • The Series ‘Topics in Molecular Organization and Engineering’ was initiated by the Symposium ‘Molecules in Physics, Chemistry, and Biology’, which was held in Paris in 1986. Appropriately dedicated to Professor Raymond Daudel, the symposium was both broad in its scope and penetrating in its detail. The sections of the symposium were: 1. The Concept of a Molecule; 2. Statics and Dynamics of Isolated Molecules; 3. Molecular Interactions, Aggregates and Materials; 4. Molecules in the Biological Sciences, and 5. Molecules in Neurobiology and So- ciobiology.

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  • This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian me- chanics and with a view to control-theoretical applications. The basic methodology is that of geometric mechanics applied to the Lagrange-d’Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case.

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  • Few of us can any longer keep up with the flood of scientific literature, even in specialized subfields. Any attempt to do more and be broadly educated with respect to a large domain of science has the appearance of tilting at windmills. Yet the synthesis of ideas drawn from different subjects into new, powerful, general concepts is as valuable as ever, and the desire to remain educated persists in all scientists.

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  • SYMMETRY CONSIDERATIONS Motor vehicles, like most machines, have a general bilateral symmetry. Only hypotheses can be advanced to explain why this occurs. Certainly to have a symmetry plane simplifies the study of the dynamic behavior of the system, for it can be modelled, within certain limits, using uncoupled equations. However, the reason is likely to be above all an aesthetic one: symmetry is considered an essential feature in most definitions of beauty.

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  • A specific example in which the theory developed here is quite crucial is the analysis of locomotion for the snakeboard, which we study in some detail in Section 8.4. The snakeboard is a modified version of a skateboard in which locomotion is achieved by using a coupling of the nonholonomic constraints with the symmetry properties of the system. For that system, traditional analysis of the complete dynamics of the system does not readily explain the mechanism of locomotion.

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  • A related modern example is the snakeboard (see LEWIS,OSTROWSKI,MURRAY &BURDICK [1994]),which shares some of the features of these examples butwhich has a crucial difference as well. This example, likemany of the others, has the sym- metry group SE(2) of Euclidean motions of the plane but, now, the corresponding momentum is not conserved. However, the equation satisfied by the momentum associated with the symmetry is useful for understanding the dynamics of the prob- lem and how group motion can be generated.

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  • Problems of nonholonomic mechanics, including many problems in robotics, wheeled vehicular dynamics and motion generation, have attracted considerable attention. These problems are intimately connected with important engineering issues such as path planning, dynamic stability, and control.Thus, the investigation of many basic issues, and in particular, the role of symmetry in such problems, remains an important subject today.

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