Hamel’s Field Variational Integrator Of Geometrically Exact Beam

Hamel’s formalism is a general representation of Lagrange mechanics by introduc-ing non-material velocity.Hamel field variational integrators are derived in Hamel’s formalism for field theories,which have good performance in preserving qualitative properties of infinite dimensional mechanical systems and can be widely applied to con-strained systems,especially those with nonholonomic constraints.In this paper,the geometrically exact beam dynamics are derived by using the Hamel field formalism,and then the discrete form of the geometrically exact beam is given by the Hamel field variational integrators.Finally,two simulations illustrates that the derived algorithm preserves energy,momentum and geometry structure in exponentially long time.