Critical Point Theory for Lagrangian Systems, Marco Mazzucchelli

Автор: Wells, D.a.
Название: Schaum`s outline of lagrangian dynamics
ISBN: 0070692580 ISBN-13(EAN): 9780070692589
Издательство: McGraw-Hill
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Описание: Includes 275 solved problems.

Автор: Gignoux
Название: Solved Problems in Lagrangian and Hamiltonian Mechanics
ISBN: 9048123925 ISBN-13(EAN): 9789048123926
Издательство: Springer
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Описание: Intends to bridge the gap between the Newtonian mechanics and the studies on chaos. This title covers such topics as: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. It is suitable for undergraduate students as well as others whose work involves mechanics, physics and engineering in general.

Автор: Claude Gignoux; Bernard Silvestre-Brac
Название: Solved Problems in Lagrangian and Hamiltonian Mechanics
ISBN: 9400791763 ISBN-13(EAN): 9789400791763
Издательство: Springer
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Описание: This work bridges the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems.

Автор: A. Ambrosetti; V. Coti-Zelati
Название: Periodic Solutions of Singular Lagrangian Systems
ISBN: 0817636552 ISBN-13(EAN): 9780817636555
Издательство: Springer
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Описание: A summary and synthesis of recent research demonstrating that variational methods can be used to successfully handle systems with singular potential, the Lagrangian systems. The classic cases of the Kepler problem and the N-body problem are used as specific examples.

Автор: A. Ambrosetti; V. Coti-Zelati
Название: Periodic Solutions of Singular Lagrangian Systems
ISBN: 1461267056 ISBN-13(EAN): 9781461267058
Издательство: Springer
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Описание: Thismonographdealswiththeexistenceofperiodicmotionsof Lagrangiansystemswith ndegreesoffreedom ij + V'(q) =0, where Visasingularpotential.Aprototypeofsuchaproblem, evenifitisnottheonlyphysicallyinterestingone, istheKepler problem .. q 0 q+yqr= . This, jointlywiththemoregeneralN-bodyproblem, hasalways beentheobjectofagreatdealofresearch.Mostofthoseresults arebasedonperturbationmethods, andmakeuseofthespecific featuresoftheKeplerpotential. OurapproachismoreonthelinesofNonlinearFunctional Analysis: ourmainpurposeistogiveafunctionalframefor systemswithsingularpotentials, includingtheKeplerandthe N-bodyproblemasparticularcases.PreciselyweuseCritical PointTheorytoobtainexistenceresults, qualitativeinnature, whichholdtrueforbroadclassesofpotentials.Thishighlights thatthevariationalmethods, whichhavebeenemployedtoob- tainimportantadvancesinthestudyofregularHamiltonian systems, canbesuccessfallyusedtohandlesingularpotentials aswell. Theresearchonthistopicisstillinevolution, andtherefore theresultswewillpresentarenottobeintendedasthefinal ones. Indeedamajorpurposeofourdiscussionistopresent methodsandtoolswhichhavebeenusedinstudyingsuchprob- lems. Vlll PREFACE Partofthematerialofthisvolumehasbeenpresentedina seriesoflecturesgivenbytheauthorsatSISSA, Trieste, whom wewouldliketothankfortheirhospitalityandsupport. We wishalsotothankUgoBessi, PaoloCaldiroli, FabioGiannoni, LouisJeanjean, LorenzoPisani, EnricoSerra, KazunakaTanaka, EnzoVitillaroforhelpfulsuggestions. May26,1993 Notation n 1.For x, yE IR, x. ydenotestheEuclideanScalarproduct, and IxltheEuclideannorm. 2. meas(A)denotestheLebesguemeasureofthesubset Aof n IR - 3.Wedenoteby ST = 0, T]/{a, T}theunitarycirclepara- metrizedby t E 0, T].Wewillalsowrite SI= ST=I. n 1 n 4.Wewillwrite sn = {xE IR +: Ixl =I}andn = IR \{O}. n 5.Wedenoteby LP( O, T], IR ),1 p +00, theLebesgue spaces, equippedwiththestandardnorm lIulip. l n l n 6. H (ST, IR )denotestheSobolevspaceof u E H,2(0, T; IR ) suchthat u(O) = u(T).Thenormin HIwillbedenoted by lIull2 = lIull + lIull - 7.Wedenoteby(-1-)and11-11respectivelythescalarproduct andthenormoftheHilbertspace E. 8.For uE E, EHilbertorBanachspace, wedenotetheball ofcenter uandradiusrby B(u, r) = {vE E: lIu- vii r}.Wewillalsowrite B = B(O, r). r 1 1 9.WesetA (n) = {uE H (St, n)}. k 10.For VE C (1Rxil, IR)wedenoteby V'(t, x)thegradient of Vwithrespectto x. l 11.Given f E C (M, IR), MHilbertmanifold, welet r = {uEM: f(u) a}, f-l(a, b) = {uE E: a f(u) b}. x NOTATION 12.Given f E C1(M, JR), MHilbertmanifold, wewilldenote by Zthesetofcriticalpointsof fon Mandby Zctheset Z U f-l(c, c). 13.Givenasequence UnE E, EHilbertspace, by Un ---"" Uwe willmeanthatthesequence Unconvergesweaklyto u. 14.With (E)wewilldenotethesetoflinearandcontinuous operatorson E. 15.With Ck''''(A, JR)wewilldenotethesetoffunctions ffrom AtoJR, ktimesdifferentiablewhosek-derivativeisHolder continuousofexponent0: . Main Assumptions Wecollecthere, forthereader'sconvenience, themainassump- tionsonthepotential Vusedthroughoutthebook. (VO) VEC1(lRXO, lR), V(t+T, x)=V(t, X) V(t, x)ElRXO, (VI) V(t, x)

Автор: Bruno Despr?s
Название: Numerical Methods for Eulerian and Lagrangian Conservation Laws
ISBN: 3319503545 ISBN-13(EAN): 9783319503547
Издательство: Springer
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Описание: This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics.

Автор: Sergey V. Prants; Michael Yu. Uleysky; Maxim V. Bu
Название: Lagrangian Oceanography
ISBN: 3319530216 ISBN-13(EAN): 9783319530215
Издательство: Springer
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Описание: This book uses the Lagrangian approach, especially useful and convenient for studying large-scale transport and mixing in the ocean, to present a detailed view of ocean circulation.

Автор: Lee, Taeyoung Leok, Melvin Mcclamroch, N. Harris
Название: Global formulations of lagrangian and hamiltonian dynamics on manifolds
ISBN: 3319569511 ISBN-13(EAN): 9783319569512
Издательство: Springer
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Описание: This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold.

Автор: V. Lakshminarayanan; Ajoy Ghatak; K. Thyagarajan
Название: Lagrangian Optics
ISBN: 1461356903 ISBN-13(EAN): 9781461356905
Издательство: Springer
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Описание: Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Given the current interest and activity in optical fibers and optical communication, analysis of light propagation in inhomogeneous media is dealt with in great detail.

Автор: Antonio Dobado; Angel Gomez-Nicola; Antonio L. Mar
Название: Effective Lagrangians for the Standard Model
ISBN: 3642638899 ISBN-13(EAN): 9783642638893
Издательство: Springer
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Описание: This book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of parti- cle physics.

Автор: Jean Mawhin
Название: Critical Point Theory and Hamiltonian Systems
ISBN: 038796908X ISBN-13(EAN): 9780387969084
Издательство: Springer
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Описание: Presents the basic tools of critical point theory such as minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds.