Challenges in the stabilization of a satellite using Controlled Lagrangians I: Gravitation

This paper intends to study the stabilization of a satellite using the method of controlled Lagrangians. The stability analysis of Euler-Poincare mechanical systems is extended to systems with non-zero potential energies. The results are then utilized in the stabilization of a satellite in a gravitational field. The effectiveness of the stabilizing law has been verified through simulations. In a sequel to this paper (Part II), we will extend the solution to an unbalanced satellite, and will discuss the capability of the method of controlled Lagrangians to cope with the issue of actuator saturation.