Welcome back. In our hydrodynamic stability series so far, we have explored methods for determining whether a flow is linearly stable or unstable. Today, we will augment these discussions by investigating two different types of instability: absolute and convective. If a flow is absolutely unstable, then a small perturbation at a particular location will grow both upstream and … [Read more...] about Hydrodynamic Stability: Absolute and Convective Instability
A Break from Engineering: The Art of the Romantic Era (c. 1830-1875)
Welcome back. In today’s blog post, let us take a break from engineering entirely and learn about the art of the Romantic Era in Europe and North America. This is an essay that I wrote as a high school sophomore in AP European History class, which to this day is the most difficult class I have ever taken. This class taught me to study hard and I owe my success in university to … [Read more...] about A Break from Engineering: The Art of the Romantic Era (c. 1830-1875)
Spring-Hinge as Simplest Model of Wing Flexibility in Efficient Propulsion
Welcome back. Today, I hope to share the introduction to the senior design project I completed last semester at USC. Hopefully it is enjoyable, and please comment if there are any questions. Until next week, please take care. Introduction: Centimeter-scale micro air vehicles (MAVs) can play valuable roles in the military and private sectors, from espionage and … [Read more...] about Spring-Hinge as Simplest Model of Wing Flexibility in Efficient Propulsion
Optimal Control with the Linear Quadratic Regulator
Welcome back. In today’s blog post, I am excited to share a bit of control theory and explore how we can use the linear quadratic regulator to obtain optimal control laws. Some questions that might come up in this exploration are: what is control theory? and what is a control system? As I understand it, control theory is the mathematical science of how we can alter the behavior … [Read more...] about Optimal Control with the Linear Quadratic Regulator
Linear Embeddings of Nonlinear Dynamics with the Koopman Operator
Welcome back. In today’s blog post, I am excited to discuss Koopman operator theory, which provides a mathematical framework for representing nonlinear dynamics as a linear system. This theory was originally developed by Columbia University professor Bernard Koopman in 1931 [1], but remained in relative obscurity until the 2000s, when modern computers allowed it to be applied … [Read more...] about Linear Embeddings of Nonlinear Dynamics with the Koopman Operator