Multisymplectic Lie group variational integrator for a geometrically   exact beam in R3
  In this paper we develop, study, and test a Lie group multisymplectic integra- tor for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions. 
Fran\c{c}ois Demoures, Fran\c{c}ois Gay-Balmaz, Marin Kobilarov, Tudor   S. Ratiu
math.NA math.DS