Eulerian and Lagrangian descriptions for the vibration analysis of a deploying beam

Abstract

In this study, the equations of motion derived from the Eulerian and Lagrangian descriptions of the vibration analysis of a deploying beam are compared and discussed. After transforming the equations to their corresponding variational equations, the discretized equations for the two descriptions are derived and their equivalence is verified. The numerical time responses obtained from the equations of both descriptions are the same. We recommend use of the Lagrangian description over the Eulerian one when analyzing the vibration of a deploying beam that includes the entirety of the beam inside and outside a rigid wall.