JERROLD E. MARSDEN
Control and Dynamical Systems 107-81
Caltech
Pasadena, CA 91125-8100
http://www.cds.caltech.edu/~marsden/
marsden@cds.caltech.edu
Abstract:
We shall discuss recent work of several people
in the area of discretizations of mechanics and
associated integration algorithms. These approaches are
based on a discrete variational principle and thereby
are automatically symplectic, momentum preserving, and
in the time adaptive case, also energy preserving.
The algorithms are obtained by quadrature
approximations of the action function. They have
excellent energy behavior even for dissipative and
forced systems. We shall discuss reduction theory for
discrete systems, with applications to satellite
dynamics. We shall also discuss some extensions of
these methods to continuum mechanics, using the notion
of multisymplectic integrators.