The long-term dynamics response of nonlinear geometrically rods undergoing finite bending, shearing and extension is considered in detail. The central objective of this work is the design of an unconditionally stable time-stepping algorithm which preserve fundamental constants of the motion namely the total linear and total angular momentums and, for the Hamiltonian case, the total energy. The variational form of the equations of motion is obtained through the Hamilton's law and its discretized spatial form is achieved by the Finite Element Method. The resulting problem is numerically solved by the new implicit time integration scheme in connection with the Newton-Raphson Method. A numerical simulation is presented in order to assess the principal features of the formulation.

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