Date of Award

Fall 2023

Document Type


Degree Name

Master of Science (MS)


Mechanical & Aerospace Engineering


Aerospace Engineering

Committee Director

Gene Hou

Committee Member

Brett Newman

Committee Member

Logan Beaver


A rigid body in space has three degrees of rotational freedom. As a result, a minimum of three independent parameters is required to define the three-dimensional orientation of a rigid body. As is well known, every set of three independent parameters has at least one orientation where mathematical or geometrical singularities are encountered; therefore, when the use of a three-parameter representation is desired, a method for singularity avoidance must also be considered. A common practice for singularity avoidance is to switch between parameter sets whose singularities occur at different orientations. With this in mind, modified Rodrigues parameters (MRP) are considered the preferred three-parameter representation, especially for large arbitrary rotations. The reason why MRP are considered the preferred choice is twofold. First, their non-singular range exceeds that of many other popular three-parameter representations; this results in less frequent switching. Second is the existence of a set of shadow MRP whose singularities occur at different orientations than the original MRP set. When the need for switching occurs, note that the same kinematic differential equations hold for both the original and shadow set of parameters, which greatly simplifies the coding required to implement a MRP solution. Note that neither the use of MRP as orientation parameters nor MRP singularity avoidance by switching between the original and shadow sets are considered new concepts; however, this study contends that existing studies do not fully explore the details concerning how the switch between the original and shadow MRP sets is achieved. As a result, this study explores various methods for achieving the switch, demonstrates their implementation, and studies their performance relative to solution accuracy and computational efficiency.


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