Abstract: Total dynamics of an airship is modeled. The body of an airship is taken as a submerged rigid body with neutral buoyancy, i.e., buoyancy with value equal to that of gravity, and the coupled dynamics between the body with ballonets and ballast is considered. The total dynamics of the airship is firstly derived by Newton-Euler laws and Kirchhoff’s equations. Furthermore, by using Hamiltonian and Lagrangian semi-direct product reduction theories, the dynamics is formulated as a Lie-Poisson system, or also an Euler-Poincaré system. These two formulations can be exploited for the control design using energy-based methods for Hamiltonian or Lagrangian system.

Key words: Kirchhoff’s equation, semi-direct product reduction, airship, dynamical modeling