Variational Structures for Hamel’s Equations and Stabilization ?

Hamel’s equations are an analogue of the Euler–Lagrange equations of Lagrangian mechanics when the velocity is measured relative to a frame which is not related to system’s local configuration coordinates. The use of this formalism often leads to a simpler representation of dynamics but introduces additional terms in the equations of motion. The paper elucidates the variational nature of Hamel’s equations and discusses their utility in control and stabilization. The latter is illustrated with the problem of stabilization of a falling disk.