Dedicated to the late Juan Carlos Simo, this volume contains the proceedings of a workshop held at the Fields Institute in October 1993. The articles focus on current algorithms for the integration of mechanical systems, from systems in celestial mechanics to coupled rigid bodies to fluid mechanics. The scope of the articles ranges from symplectic integration methods to energy-momentum methods and related themes.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians, physicists, astrophysicists, and engineers interested in mechanics of particles and systems.

Table of Contents

• F. Armero and J. Simo -- Formulation of a new class of fractional-step methods for the incompressible MHD equations that retains the long-term dissipativity of the continuum..
• E. J. Barth and B. J. Leimkuhler -- Symplectic methods for conservative multibody systems
• P. J. Channell and F. R. Neri -- An introduction to symplectic integrators
• A. J. Dragt and D. T. Abell -- Symplectic maps and computation of orbits in particle accelerators
• D. J. D. Earn and A. Lichtenberg -- Arnold diffusion in symplectic lattice maps
• M. Kaasalainen and J. Binney -- Integrable Hamiltonians from close approximations to invariant tori
• P. V. Koseleff -- Exhaustive search of symplectic integrators using computer algebra
• D. K. Lewis and J. Simo -- Conserving algorithms for the \(N\) dimensional rigid body
• R. I. McLachlan -- More on symplectic correctors
• R. I. McLachlan and C. Scovel -- A survey of open problems in symplectic integration
• S. Reich -- Symplectic integrators for systems of rigid bodies
• J. M. Sanz-Serna -- Backward error analysis of symplectic integrators
• T. J. Stuchi and R. Vieira-Martins -- Numerical determination of caustics and their bifurcations
• J. Wisdom, M. Holman, and J. Touma -- Symplectic correctors