Foundations of the Geometric Mechanics Udwadia-Kalaba Framework for Rigid Body Constrained Motion Analysis

<p>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.</p>

Name thesis:degree_name

Master of Science in Aerospace Engineering

Level thesis:degree_level

Thesis - Open Access

Discipline thesis:degree_discipline

Aerospace Engineering

Year

2020

Author dc:creator

• McCann, Brennan S.

• mechanics
• Udwadia-Kalaba
• rigid body
• constrained
• motion
• Aerospace Engineering
• Engineering Physics

Repository record dc:identifier

https://commons.erau.edu/edt/556

OAI identifier oai:identifier

oai:commons.erau.edu:edt-1559