Lagrangian description of the variational equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. After discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system.