What This Document Is
This document contains a completed solution set for Homework Assignment 11 of AAE 34000, Dynamics and Vibrations, at Purdue University. It was originally completed in Fall 2012 and updated in 2014. The assignment focuses on the derivation and application of Euler’s equations of motion, both for principal and non-principal axes.
Why This Document Matters
This solution set is intended for students enrolled in AAE 34000 who are seeking to check their work on Homework 11. It provides a detailed walkthrough of the problems, offering insights into the expected approach and correct answers. It’s most useful after a student has attempted the problems independently and is looking for clarification or confirmation.
Common Limitations or Challenges
This document is a completed assignment; it does not provide instruction on *how* to solve the problems. It assumes the user has a foundational understanding of the course material and is using the solution as a verification tool. It will not substitute for attending lectures, reading the textbook, or actively engaging with the course concepts.
What This Document Provides
The full document includes:
* Derivation of Euler’s equations of motion for non-principal axes.
* Simplification of Euler’s equations assuming principal axes.
* State-space representation of Euler’s equations for principal axes.
* Numerical solutions for angular velocities (Wx, Wy, Wz) and angular momentum components (Hx, Hy, Hz) for an axisymmetric spacecraft.
* Plots illustrating the time-varying behavior of angular velocities and angular momentum.
* MATLAB code used to generate the numerical solutions.
This preview does *not* include the full derivations, numerical results, or MATLAB code. It only provides a high-level overview of the assignment’s content.