Sökning: "second-order ordinary differential equation"

Hittade 4 uppsatser innehållade orden second-order ordinary differential equation.

  1. 1. Physics-Informed Deep Learning for System Identification of Autonomous Underwater Vehicles : A Lagrangian Neural Network Approach

    Master-uppsats, KTH/Skolan för elektroteknik och datavetenskap (EECS)

    Författare :Badi Mirzai; [2021]
    Nyckelord :AUV; System Identification; Deep Learning; Physics-Informed Deep Learning; Lagrangian Neural Networks; AUV; System Identifiering; Djupinlärning; Fysik-Informerad Djupinlärning; Lagrangianska Neurala Nätverk;

    Sammanfattning : 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. LÄS MER

  3. 2. An introduction to some ordinary differential equations governing stellar structures

    Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Författare :Yani di Giovanni; [2019]
    Nyckelord :Mathematics and Statistics;

    Sammanfattning : 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. LÄS MER

  4. 3. Beräkningsmetoder för Molekylsimuleringar

    Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

    Författare :Viktor Sandström; [2019]
    Nyckelord :;

    Sammanfattning : Denna avhandling handlar om beräkningsmetoder för att utföra molekylsimuleringar på ett system av enkla partiklar. Genom att använda Lennard-Jones parpotential kan den attraktiva-repulsiva kraften som verkar på atomer och molekyler modelleras. LÄS MER

  5. 4. Equivalence Group of Lie's Second-Order Equation of Type III

    Master-uppsats, Blekinge Tekniska Högskola/Sektionen för ingenjörsvetenskap

    Författare :Dai Jiayuan; [2012]
    Nyckelord :equivalence transformation; second-order ordinary differential equation; principal Lie algebra;

    Sammanfattning : 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. LÄS MER