We propose in this paper a general analytic scheme based on Gauss principle of least constraint for the derivation of the Lagrangian dynamics equation of motion of arbitrarily parameterized free-floating-base articulated mechanisms. The free-floating base of the mechanism is a non-actuated rigid object evolving in the 6D Lie group SE(3), the SO(3) component of which can be parameterized using arbitrary coordinate charts with equality constraints, for instance unit quaternions (also known as Euler parameters). This class of systems includes humanoid robots, and the presented formalism is particularly suitable for the whole-body dynamics modeling and control problem of such humanoid systems. Example motions of humanoid in arbitrary contact states with the environment demonstrate the originality of the approach.