1549055384-Symplectic_Geometry_and_Topology__Eliashberg_

LECTURE 5. VARIATIONAL INTEGRATORS 407 Given a solution q(t) E CL, a first variation at q(t) is a vector field V on Q along q(t) ...

408 J .E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY qi: Q x Q--+ Q x Q by F(q 1 ,qo) = (q2,q 1 ), where q2 is found from the di ...

LECTURE 5. VARIATIONAL INTEGRATORS 409 So there are two generally distinct 1-forms, but (up to sign) only one 2-form. If we make ...

410 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Definition 5.6. The dual jet bundle J^1 (Y)* is the vector bundle over Y who ...

LECTURE 5. VARIATIONAL INTEGRATORS 411 for a (local) section <P of Y. The left hand side of (5.46) is often denoted 8L/8¢A an ...

412 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY of the multisymplectic and Noether theorem structure directly from the varia ...

Bibliography Abarbanel, H.D.I. and D.D. Holm [1987] Nonlinear stability analysis of in- viscid flows in three dimensions: incom ...

414 J. E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Armero, F. and J.C. Simo [1993] A-Priori Stability Estimates and Uncondi- ...

BIBLIOGRAPHY 415 Barth, E. and Leimkuhler, B. [1996b]. Symplectic methods for conservative multibody systems. Fields Institute ...

416 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Bridges, T.J. [1994] Hamiltonian spatial structure for 3D water waves relat ...

BIBLIOGRAPHY 417 Clebsch, A. [1857] Uber eine allgemeine Transformation der hydrodynamis- chen Gleichungen, Z. Reine Angew. Mat ...

418 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Ge, Z. and J.E. Marsden [1988] Lie-Poisson integrators and Lie-Poisson Hami ...

BIBLIOGRAPHY 419 Guillemin, V. and S. Sternberg [1980] The moment map and collective motion, Ann. of Phys. 1278 , 220-253. Guil ...

420 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Holmes, P.J. and J.E. Marsden [1978] Bifurcation to divergence and flutter ...

BIBLIOGRAPHY 421 132. Koon, W.S. and J.E. Marsden [1998b] The Geometric Structure of Nonholo- nomic Mechanics, Proc. CDC, San Di ...

422 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Leonard, N.E. [1995b] P eriodic forcing, dynamics and control of underactu- ...

BIBLIOGRAPHY 423 Low, F.E. [1958] A Lagrangian formulation of the Boltzmann-Vlasov equation for plasmas, Proc. Roy. Soc. Land. ...

424 J.E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY Marsden, J.E., T.S. Ratiu, and A. Weinstein [1984a] Semi-direct products an ...

BIBLIOGRAPHY 425 Meyer, K.R. [1973] Symmetries and integrals in mechanics, in Dynamical Systems, M. Peixoto (ed.) , Academic P ...

426 J. E. MARSDEN, MECHANICS, DYNAMICS, AND SYMMETRY O 'Reilly, 0, N .K. Malhotra and N.S. Namamchchivaya [1996] Some aspects o ...