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Full-Text Articles in Dynamical Systems
Comparison Of Linear Control Techniques For The Underactuated Nonlinear Quadcopter System, Ian Golsby
Comparison Of Linear Control Techniques For The Underactuated Nonlinear Quadcopter System, Ian Golsby
Mathematics Senior Capstone Papers
Uncrewed Aerial Vehicles (UAVs) are a prevalent technology in many fields. They must be lightweight, efficient, and stable in order to carry out their objectives or support a payload. The control system that maintains a UAV’s attitude directly contributes to the stability and efficiency of the UAV, and more efficient UAVs can be made more lightweight by reducing battery size. Because the UAV has only four degrees of control (one per motor) but requires twelve dimensions to describe its orientation and position over time, it is considered an under-actuated nonlinear complex system. In this study, we compare various linear control …
Periodic Points And Sharkovsky’S Theorem, Luke J. Seaton
Periodic Points And Sharkovsky’S Theorem, Luke J. Seaton
Mathematics Senior Capstone Papers
The number of periodic points of a function depends on the context. The number of complex periodic points and rational periodic points have been shown to be infinite and finite, respectively, if f is a polynomial of degree at least 2. However, the number of real periodic points can be either finite or infinite. Sharkovskys Theorem states that if p is left of q in the “Sharkovsky ordering” and the continuous function f has a point of period p, then f also has a point of period q. This statement becomes very powerful when considering a function that has points …
The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano
The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano
Mathematics Senior Capstone Papers
The SIR (Susceptible-Infected-Recovered) models are used to help predict the spread of diseases. The goals of this paper are: elaborating on the methods of approximating the recovery rate, infection rate, and loss of immunity rate, comparing the SIR models with these approximation methods to real world data, and determining the most accurate combination of the approximation methods for each SIR model. There are several SIR models such as the Kermack-McKendrick, SIRS, and SI models that are designed for specific diseases. Understanding the parameters of these models will assist us in maximizing their accuracy. For example, there is no explicit formula …