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
An Introduction to Flight
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
Hydrodynamic Stability: Three-Dimensional Linear Stability and Input-Output Analysis of Parallel Shear Flows
Introduction: Welcome back. Today, I am excited to return to our series on hydrodynamic stability. In previous blogs, we considered the stability of two-dimensional parallel shear flows. Now, we will derive the governing equations for stability analysis of three-dimensional parallel shear flows. Our mathematical work here will give us the tools to consider oblique modes and … [Read more...] about Hydrodynamic Stability: Three-Dimensional Linear Stability and Input-Output Analysis of Parallel Shear Flows
Water Channel Dye Visualization Experiments – Fall 2023
Welcome back. This week, I hope to continue our break from the regular hydrodynamic stability program and share a project I worked on last fall. This work involved water channel dye visualization experiments to reveal the locations of flow separation and reattachment on the cambered NACA 65(1)-412 airfoil at transitional Reynolds numbers Re ∈ [104, 105]. These experiments fit … [Read more...] about Water Channel Dye Visualization Experiments – Fall 2023