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Books on the topic 'Système Lagrangien'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Mielke, Alexander. Hamiltonian and Lagrangian flows on center manifolds: With applications to elliptic variational problems. Berlin: Springer-Verlag, 1991.

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2

service), SpringerLink (Online, ed. Critical Point Theory for Lagrangian Systems. Basel: Springer Basel AG, 2012.

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3

Ambrosetti, A. Periodic solutions of singular Lagrangian systems. Boston: Birkhäuser, 1993.

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4

Ambrosetti, Antonio, and Vittorio Coti Zelati. Periodic Solutions of Singular Lagrangian Systems. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0319-3.

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5

Mazzucchelli, Marco. Critical Point Theory for Lagrangian Systems. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0163-8.

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6

An introduction to Lagrangian mechanics. 2nd ed. Hackensack,] New Jersey: World Scientific, 2015.

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7

Brizard, Alain Jean. An introduction to Lagrangian mechanics. Hackensack, NJ: World Scientific, 2008.

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8

Brizard, Alain Jean. An introduction to Lagrangian mechanics. Hackensack, NJ: World Scientific, 2008.

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9

An introduction to Lagrangian mechanics. Hackensack, NJ: World Scientific, 2008.

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10

Lagrangian and Hamiltonian mechanics. Singapore: World Scientific, 1996.

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11

Deriglazov, Alexei. Classical mechanics: Hamiltonian and Lagrangian Formalism. Berlin: Springer Verlag, 2010.

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12

Kamada, Ray. Chaos metrics for testing Lagrangian particle models. Monterey, Calif: Naval Postgraduate School, 1993.

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13

Classical mechanics: Hamiltonian and Lagrangian Formalism. Berlin: Springer Verlag, 2010.

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14

Mušicki, Đorđe. Degenerate systems in generalized mechanics. Beograd: Matematički Institut, 1992.

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15

Mušicki, Đorđe. Degenerate systems in generalized mechanics. Beograd: Matematički Institut, 1992.

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16

Bernard, Silvestre-Brac, and SpringerLink (Online service), eds. Solved Problems in Lagrangian and Hamiltonian Mechanics. Dordrecht: Springer Netherlands, 2009.

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17

Ortega, Romeo, Antonio Loría, Per Johan Nicklasson, and Hebertt Sira-Ramírez. Passivity-based Control of Euler-Lagrange Systems. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-3603-3.

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18

Gans, Roger F. Engineering Dynamics: From the Lagrangian to Simulation. New York, NY: Springer New York, 2013.

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19

L, Mangiarotti, and Sardanashvili G. A, eds. New Lagrangian and Hamiltonian methods in field theory. Singapore: World Scientific, 1997.

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20

Lagrangian and Hamiltonian mechanics: Solutions to the exercises. Singapore: World Scientific, 1999.

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21

Șandru, Ovidiu-Ilie. Local Hamilton-Lagrange structures: Applications in the partial differential equations theory. Timișoara: Universitatea din Timișoara, Facultatea de Matematică, 1994.

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22

Francesco, Bullo, and Fujimoto Kenji 1947-, eds. Lagrangian and Hamiltonian methods for nonlinear control 2006: Proceedings from the 3rd IFAC workshop, Nagoya, Japan, July 2006. Berlin: Springer, 2007.

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23

A, Astolfi, Gordillo Francisco 1964-, Schaft, A. J. van der, and International Federation of Automatic Control, eds. Lagrangian and Hamiltonian methods for nonlinear control 2003: A proceedings volume from the 2nd IFAC Workshop, Seville, Spain, 3-5 April, 2003. Oxford: Published for the International Federation of Automatic Control by Elsevier, 2003.

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24

IFAC Workshop (2000 Princeton, N.J.). Lagrangian and Hamiltonian methods for nonlinear control: A proceedings volume from the IFAC Workshop, Princeton, New Jersey, USA, 16-18 March 2000. Oxford: Pergamon, 2000.

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25

Generalized Hamiltonian formalism for field theory: Constraint systems. Singapore: World Scientific, 1995.

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26

Baldomá, Inmaculada. Exponentially small splitting of invariant manifolds of parabolic points. Providence, RI: American Mathematical Society, 2004.

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27

Ordinary differential equations: Qualitative theory. Providence, R.I: American Mathematical Society, 2010.

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28

author, Winternitz Pavel, ed. Classification and identification of Lie algebras. Providence, Rhode Island: American Mathematical Society, 2014.

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29

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. Providence, R.I: American Mathematical Society, 2012.

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30

1980-, Blazquez-Sanz David, Morales Ruiz, Juan J. (Juan José), 1953-, and Lombardero Jesus Rodriguez 1961-, eds. Symmetries and related topics in differential and difference equations: Jairo Charris Seminar 2009, Escuela de Matematicas, Universidad Sergio Arboleda, Bogotá, Colombia. Providence, R.I: American Mathematical Society, 2011.

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31

Mann, Peter. Near-Integrable Systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0024.

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This chapter extends the now familiar Lagrangian formulation to a field theory and covers elementary material in this new setting. The motion of systems with a very large number of degrees of freedom makes it necessary to specify an almost infinite number of discrete coordinates. It is possible to simplify the situation by taking the continuum limit, which replaces the individual coordinates with a continuous function that describes a displacement field, which assigns a displacement vector to each position the system could occupy relative to an equilibrium configuration. The field thus takes a point in the spacetime manifold and assigns it a value corresponding to whatever the field represents. In this chapter, many interdisciplinary examples are solved and pedagogical models are discussed. The chapter also discusses Lagrange density, the Lagrange field equation, instantons, the Klein–Gordon equation, Fourier transforms and the Korteweg–de Vries equation.

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32

Mann, Peter. Lagrangian and Hamiltonian Dynamics. Oxford University Press, 2018.

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33

Mann, Peter. Lagrangian and Hamiltonian Dynamics. Oxford University Press, 2018.

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34

A Students Guide To Lagrangians And Hamiltonians. Cambridge University Press, 2013.

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35

Ambrosetti, A. Periodic Solutions of Singular Lagrangian Systems. Springer, 2013.

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36

Mazzucchelli, Marco. Critical Point Theory for Lagrangian Systems. Springer, 2011.

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37

Mann, Peter. Point Transformations in Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0009.

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This chapter discusses point transformations in Lagrangian mechanics. Sometimes, when solving problems, it is useful to change coordinates in velocity phase space to better suit and simplify the system at hand; this is a requirement of any physical theory. This change is often motivated by some experimentally observed physicality of the system or may highlight new conserved quantities that might have been overlooked using the old description. In the Newtonian formalism, it was a bit of a hassle to change coordinates and the equations of motion will look quite different. In this chapter, point transformations in Lagrangian mechanics are developed and the Euler–Lagrange equation is found to be covariant. The chapter discusses coordinate transformations, parametrisation invariance and the Jacobian of the transform. Re-parametrisations are also included.

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38

Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.

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39

Mann, Peter. The Jacobi Energy Function. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0010.

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This chapter focuses on the Jacobi energy function, considering how the Lagrange formalism treats the energy of the system. This discussion leads nicely to conservation laws and symmetries, which are the focus of the next chapter. The Jacobi energy function associated with a Lagrangian is defined as a function on the tangent bundle. The chapter also discuss explicit vs implicit time dependence, and shows how time translational invariance ensures the generalised coordinates are inertial, meaning that the energy function is the total energy of the system. In addition, it examines the energy function using non-inertial coordinates and explicit time dependence.

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40

Deriglazov, Alexei. Classical Mechanics: Hamiltonian and Lagrangian Formalism. Springer, 2018.

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41

Deriglazov, Alexei. Classical Mechanics: Hamiltonian and Lagrangian Formalism. Springer, 2016.

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42

Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (Interdisciplinary Applied Mathematics). Springer, 2006.

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43

Gignoux, Claude, and Bernard Silvestre-Brac. Solved Problems in Lagrangian and Hamiltonian Mechanics. Springer, 2014.

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44

A Students Guide to Lagrangians and Hamiltonians. Cambridge University Press, 2013.

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45

Gans, Roger F. Engineering Dynamics: From the Lagrangian to Simulation. Springer, 2016.

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46

Giachetta, G., G. Sardanashvily, and L. Mangiarotti. New Lagrangian and Hamiltonian Methods in Field Theory. World Scientific Pub Co Inc, 1994.

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47

Lagrangian and Hamiltonian Mechanics: Solutions to the Exercises. World Scientific Publishing Company, 1999.

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48

Wiggins, Stephen, and Roger M. Samelson. Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach. Springer, 2010.

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49

Lagrangian Reduction by Stages (Memoirs of the American Mathematical Society). American Mathematical Society, 2001.

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50

Leonard, N. E., and R. Ortega. Lagrangian and Hamiltonian Methods for Nonlinear Control 2000 (IFAC Proceedings Volumes). Pergamon, 2000.

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