Multisymplectic Lie group variational integrator for a geometrically exact beam in R3R3

• We discretize the covariant formulation of the geometrically exact beam model.
• The discrete covariant principle is established on a triangular spacetime discretization.
• Noether’s theorem and discrete covariant Euler–Lagrange equations are developed.
• The multisymplectic integrator is symplectic in both time and space discrete evolutions.
• Several tests illustrate time and space evolution, as well as reconstruction.

In this paper we develop, study, and test a Lie group multisymplectic integrator 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.