Lagrangian Derivation of Variable-Mass Equations of Motion using an Arbitrary Attitude Parameterization

Lagrange's equation is a popular method of deriving equations of motion due to the ability to choose a variety of generalized coordinates and implement constraints. When using a Lagrangian formulation, part of the generalized coordinates may describe the attitude. This paper presents a means of deriving the dynamics of variable-mass systems using Lagrange's equation while using an arbitrary constrained attitude parameterization. The equivalence to well-known forms of the equations of motion is shown.