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Lagrange Days  | enregistrements trouvés : 8

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Everything is under control: mathematics optimize everyday life.
In an empirical way we are able to do many things with more or less efficiency or success. When one wants to achieve a parallel parking, consequences may sometimes be ridiculous... But when one wants to launch a rocket or plan interplanetary missions, better is to be sure of what we do.
Control theory is a branch of mathematics that allows to control, optimize and guide systems on which one can act by means of a control, like for example a car, a robot, a space shuttle, a chemical reaction or in more general a process that one aims at steering to some desired target state.
Emmanuel Trélat will overview the range of applications of that theory through several examples, sometimes funny, but also historical. He will show you that the study of simple cases of our everyday life, far from insignificant, allow to approach problems like the orbit transfer or interplanetary mission design.
control theory - optimal control - stabilization - optimization - aerospace - Lagrange points - dynamical systems - mission design
Everything is under control: mathematics optimize everyday life.
In an empirical way we are able to do many things with more or less efficiency or success. When one wants to achieve a parallel parking, consequences may sometimes be ridiculous... But when one wants to launch a rocket or plan interplanetary missions, better is to be sure of what we do.
Control theory is a branch of mathematics that allows to control, optimize and guide systems on ...

49J15 ; 93B40 ; 93B27 ; 93B50 ; 65H20 ; 90C31 ; 37N05 ; 37N35

The most important works of the young Lagrange were two very learned memoirs on sound and its propagation. In a tour de force of mathematical analysis, he solved the relevant partial differential equations in a novel manner and he applied the solutions to a number of acoustic problems. Although Euler and d'Alembert may have been the only contemporaries who fully appreciated these memoirs, their contents anticipated much more of Fourier analysis than is usually believed. On the physical side, Lagrange properly explained the functioning of string and air-column instruments, although he did not accept harmonic analysis as we now understand it.
Lagrange - acoustics - propagation of sound - harmonic analysis - Fourier analysis - vibrating strings - organ pipes
The most important works of the young Lagrange were two very learned memoirs on sound and its propagation. In a tour de force of mathematical analysis, he solved the relevant partial differential equations in a novel manner and he applied the solutions to a number of acoustic problems. Although Euler and d'Alembert may have been the only contemporaries who fully appreciated these memoirs, their contents anticipated much more of Fourier analysis ...

01A50 ; 35-03 ; 40-03 ; 76-03

Mathematical modeling and numerical mathematics of today is very much Lagrangian and modern automated modeling techniques lead to differential-algebraic systems. The optimal control for such systems in general cannot be obtained using the classical Euler-Lagrange approach or the maximum principle, but it is shown how this approach can be extended.
differential-algebraic equations - optimal control - Lagrangian subspace - necessary optimality conditions - Hamiltonian system - symplectic flow
Mathematical modeling and numerical mathematics of today is very much Lagrangian and modern automated modeling techniques lead to differential-algebraic systems. The optimal control for such systems in general cannot be obtained using the classical Euler-Lagrange approach or the maximum principle, but it is shown how this approach can be extended.
differential-algebraic equations - optimal control - Lagrangian subspace - necessary optimality ...

93C05 ; 93C15 ; 49K15 ; 34H05

Lagrange - history of mathematics - 19th century - fluid mechanics

01A55 ; 70H03 ; 76M30 ; 76B15

Multi angle  When he was one hundred years old!
Verdier, Norbert (Auteur de la Conférence) | CIRM (Editeur )

In this talk we will don't speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange's reception at the nineteenth Century. "Who read Lagrange at this Times?", "Why and How?", "What does it mean being a mathematician or doing mathematics at this Century" are some of the questions of our conference. We will give some elements of answers and the case Lagrange will be a pretext in order to explain what are doing historians of mathematics: searching archives and ­ thanks to a methodology ­ trying to understand, read and write the Past.
Lagrange - mathematical press - complete works - bibliographic index of mathematical sciences (1894-1912) - Liouville - Boussinesq - Terquem
In this talk we will don't speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange's reception at the nineteenth Century. "Who read Lagrange at this Times?", "Why and How?", "What does it mean being a mathematician or doing mathematics at this Century" are some of the questions of our conference. We will give some elements of answers and the case Lagrange will be a pretext in order to explain what are doing historians of mathematics: ...

01A50 ; 01A55 ; 01A70 ; 01A74 ; 01A80

Multi angle  On the discovery of Lagrange multipliers
Wanner, Gerhard (Auteur de la Conférence) | CIRM (Editeur )

Multi angle  Lagrange and water waves
Saut, Jean-Claude (Auteur de la Conférence) | CIRM (Editeur )

Lagrange - 19th century - water waves

01A55 ; 76B15

Multi angle  Billiard and rigid rotation
Treschev, Dmitry (Auteur de la Conférence) | CIRM (Editeur )

Can a billiard map be locally conjugated to a rigid rotation? We prove that the answer to this question is positive in the category of formal series. We also present numerical evidence that for "good" rotation angles the answer is also positive in an analytic category.
billiard systems # integrable Hamiltonian systems # normal form convergence # small divisors # elliptic fixed point # analytic conjugacy

37D50 ; 70H06

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