Date of Award
Fall 12-2020
Access Type
Thesis - Open Access
Degree Name
Master of Science in Aerospace Engineering
Department
Aerospace Engineering
Committee Chair
Morad Nazari
First Committee Member
Sergey V. Drakunov
Second Committee Member
Troy Henderson
Third Committee Member
Richard Prazenica
Abstract
Presented herein are multiple tools for constrained motion analysis extended to different dynamical frameworks. The Udwadia-Kalaba (UK) formalism for the constrained motion analysis of a point mass is a well-documented and applied methodology. Here, UK formulation is generalized to the dynamics of rigid bodies on nonlinear manifolds in the geometric mechanics framework. This approach simultaneously treats rotational and translational motion in a unified method without encountering singularites or non-uniqueness, issues that would arise were attitude parameterization sets used. The viability of this geometric mechanics UK formalism is demonstrated for the cases of fully and underconstrained systems. The nominal UK formalism requires the complete knowledge of the system dynamics. In the presence of unmodeled dynamics or uncertainties in the system, the stability of the system cannot be assessed using the nominal UK formulation. Therefore, a controller is presented that stabilizes the system under unmodeled dynamics and external perturbations. In addition, the UK formulation has been historically applied to systems with equality constraints. However, it has not been formulated for usage with inequality constraints. Here, the implementation of slack and excess variables to treat this class of constraints is presented for usage within the UK formulation for the point mass constrained motion with inequality constraints. Also contained within is an extension of pre-existing work which models the gravitational force acting on a rigid body from a nonuniform gravitational field that holds for any degree and order of spherical harmonics.
Scholarly Commons Citation
McCann, Brennan S., "Foundations of the Geometric Mechanics Udwadia-Kalaba Framework for Rigid Body Constrained Motion Analysis" (2020). Doctoral Dissertations and Master's Theses. 556.
https://commons.erau.edu/edt/556