Lagrangian modelling

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  • Introduction to hydrodynamic modelling and granular dynamics The present text introduces hydrodynamic modelling principles in the context of batch wet granulation and coating systems and it reviews the latest achievements and proposals in the scientific literature in this field. The text concerns primarily the Eulerian and the Lagrangian modelling technique. In accordance with some of the latest published Ph.d. thesis in the field of hydrodynamics modelling, the Lagrangian technique is divided into a soft-particle and a hardsphere approach.

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  • We describe an exact decoding algorithm for syntax-based statistical translation. The approach uses Lagrangian relaxation to decompose the decoding problem into tractable subproblems, thereby avoiding exhaustive dynamic programming. The method recovers exact solutions, with certificates of optimality, on over 97% of test examples; it has comparable speed to state-of-the-art decoders.

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  • The last decades have marked the beginning of a new era in Celestial Mechanics. The challenges came from several different directions. The stability theory of nearly–integrable systems (a class of problems which includes many models of Celestial Mechanics) profited from the breakthrough represented by the Kolmogorov– Arnold–Moser theory, which also provides tools for determining explicitly the parameter values allowing for stability.

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  • A long-term goal of our work is to develop the basic control theory for me- chanical systems, and Lagrangian systems in particular. There are several reasons why mechanical systems are good candidates for new results in nonlinear control. On the practical end, mechanical systems are often quite well identified, and ac- curate models exist for specific systems, such as robots, airplanes, and spacecraft.

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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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