Computational Geometric Mechanics and Control of Rigid Bodies

iii ACKNOWLEDGEMENTS It has been a blessing to me that I could do what I really like to do under encouragements and supports from my family and friends. As everybody says, a graduation implies a new challenge, which makes me excited and thrilled. But, before setting out on my new journey of academia, I would like to express my gratitude to who have influenced on me. From the very beginning, my parents have inspired me with courage: when I made any decision, they always supported me and deduced several reasons that made the decision more appropriate. Now, I understand a little bit about raising a child with absolute trust, instead of having expectations or concerning about him. It is easy to tell an instructive story to a child, but it requires a tremendous effort to teach a child by showing a real model of what he ought to be. My parents have been doing it for me ever since I was born, and I am really proud of my parents. I have had another exclusive privilege of being advised by Professor N. Harris McClamroch and Professor Melvin Leok. It has been an honor to have an academic guidance, instruction, encourage-ment, and insight from both of them, throughout my doctoral study. I am aware that, in some cases