Modeling of Constrained Variable Mass Systems Based Upon the Boltzmann-Hamel Approach

Abstract The paper details derivation of the Boltzmann-Hamel equations modified to encompass variable mass and inertia systems that are constrained by holonomic or nonholonomic constraints. The motivations to modify the original equations derived for unconstrained constant mass systems are the equations advantages in modeling moving systems, i.e. they can be derived in body fixed frames, the modeling parameters are quasi-velocities that can be selected arbitrarily and as such can satisfy the constraint equations. Also, there is a need for obtaining unified dynamics and control frameworks for variable mass systems, e.g. an inertia-propelled underwater vehicle, which illustrates the theoretical development in the paper. The vehicle is propelled by the change of mass in its water tanks and motion of a movable mass enables maneuverings. Also, the vehicle may be constrained by kinematic or programmed constraints. The typical approach to modeling of variable mass systems is based upon the Newton-Euler or Lagrange constant mass systems approaches, in which the change of mass is additionally added. The general dynamics framework for variable mass and inertia systems developed in the paper is based upon the Boltzmann-Hamel equations. It is free of the constraint reaction forces and can be directly apply to generate dynamics control models. The Boltzmann-Hamel equations are applied to prove its effectiveness in analyses of motion performance of an underwater inertia-propelled vehicle model.