YoVDO

Quaternions for Rotation, Axis-Angle, Euler Parameters - MATLAB Examples - Rodrigues Rotation Formula

Offered By: Ross Dynamics Lab via YouTube

Tags

Aerospace Engineering Courses MATLAB Courses Quaternion Courses Spacecraft Dynamics Courses

Course Description

Overview

Explore the intricacies of quaternions, axis-angle representation, and Euler parameters in this comprehensive lecture on space vehicle dynamics. Delve into the axis-angle representation of rotation based on Euler's rotation theorem, and understand how quaternions, specifically Euler parameters, relate to the four elements of a quaternion derived from axis and angle. Learn about the rotation matrix (direction cosine matrix) and its parameterization using Euler angles and axis-angle pairs. Discover why the 4-dimensional Euler parameters offer advantages over other representations due to their non-singular nature and well-behaved kinematics differential equation. Follow along with MATLAB tutorials demonstrating practical applications of these concepts, including calculations for axis-angle representation, conversion between axis-angle and rotation matrix, and Euler parameters to rotation matrix transformations.

Syllabus

Review of previous attitude descriptions.
Numerical demonstration of axis angle description of rotation of Space Shuttle .
From rotation matrix to axis-angle.
MATLAB tutorial for calculating axis-angle based on example from Schaub & Junkins book.
Going from axis-angle to rotation matrix (Direction Cosine Matrix).
MATLAB tutorial for axis-angle to rotation matrix .
Kinematic differential equations for axis-angle set.
Euler parameters, elements of the quaternion.
MATLAB tutorial for Euler parameters to rotation matrix.
Additional problems for practice.


Taught by

Ross Dynamics Lab

Related Courses

Scientific Computing
University of Washington via Coursera
Dynamical Modeling Methods for Systems Biology
Icahn School of Medicine at Mount Sinai via Coursera
Elements of Structures
Massachusetts Institute of Technology via edX
Analyse numérique pour ingénieurs
École Polytechnique Fédérale de Lausanne via Coursera
Dynamics
Massachusetts Institute of Technology via edX