Essays about: "second-order ordinary differential equation"
Found 3 essays containing the words second-order ordinary differential equation.
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1. Physics-Informed Deep Learning for System Identification of Autonomous Underwater Vehicles : A Lagrangian Neural Network Approach
University essay from KTH/Skolan för elektroteknik och datavetenskap (EECS)Abstract : In this thesis, we explore Lagrangian Neural Networks (LNNs) for system identification of Autonomous Underwater Vehicles (AUVs) with 6 degrees of freedom. One of the main challenges of AUVs is that they have limited wireless communication and navigation under water. READ MORE
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2. An introduction to some ordinary differential equations governing stellar structures
University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : The Lane-Emden equation is a non-linear differential equation governing the equilibrium of polytropic stationary self-gravitating, spherically symmetric star models; $${\frac {1}{\xi ^{2}}}{\frac {d}{d\xi }}\left({\xi ^{2}{\frac {d\theta }{d\xi }}}\right)+\theta ^{n}=0.$$ In the isothermal cases we have the Chandrasekhar equation: $${\frac {1}{\xi ^{2}}}{\frac {d}{d\xi }}\left({\xi ^{2}{\frac {d\psi}{d\xi }}}\right)-e^{-\psi}=0$$ After having derived these models, we will go through all cases for which analytic solutions are achievable. READ MORE
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3. Equivalence Group of Lie's Second-Order Equation of Type III
University essay from Blekinge Tekniska Högskola/Sektionen för ingenjörsvetenskapAbstract : Based on symmetry and invariance principles, Lie group analysis is the only systematic method for solving nonlinear differential equations analytically. Nonlinear second-order ordinary differential equations admitting two-dimensional Lie algebras can be transformed into one of the four types of canonical forms via Lie's integration method. READ MORE
