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Showing 1 to 16 of 16 for “"Lagrange equations"”.
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Invariant Euler-Lagrange Equations for Variational Problems Defined over Framed Curves in Two and Three Dimensions
… deriving and understanding the invariant Euler-Lagrange equations for variational problems defined over framed curves in two and three dimensions. We make use of the moving frame machinery developed by Fels and Olver ([FO99]) along with the structure of the invariant variational complex as …
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Geometric discretization schemes and differential complexes for elasticity
… this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers.
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Tipping Points in Stochastically Perturbed Linear Filippov Systems
… using solutions to the corresponding Euler-Lagrange equations and a gradient flow applied to the functional. We also prove an extension of Kramer's law to determine bounds for the expected tipping time. Using these methods, we determine the most probable transition path from a frozen state …
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Mathematical modeling, trajectory and vibrations control of a three link flexible robot
… and control of a three link flexible robot. The Lagrange equations are used for deriving the equations of motion of this three link flexible robot. The equations of motion of this robot are derived by using a mathematical and symbolic manipulation software known as MACSYMA. The vibration mode …
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Differential and Integral Invariance of the Relativistic Vlasov-Boltzmann Equation and the Associated Invariant Variational Problem
Relativistic Vlasov-Boltzmann kinetic equations are constructed from quantum field theory for scalar bosons and Dirac fermion fields. Lie's principle of differential invariance is extended to the case of non-linear integro-differential equations for both scalar and matrix distribution functions, …
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Dynamic analysis of a marine riser
… a marine riser is considered in this thesis. The equations of motion for a marine riser undergoing large three dimensional deflections and rotations are derived using modal discretization approach. The nonlinear expressions for the bending and torsional deformations are obtained for a beam …
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Lagrangian structures and multidimensional consistency
… a volume form), which through the Euler-Lagrange equations provides us with one single equation (i.e., one per component of the dependent variable). Multidimensional consistency is a key integrability property of certain discrete systems; it implies that we are dealing with infinite …
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Development of a nonlinear predictive control algorithm and its application to flotation
… optimal control problems, applying the Euler-Lagrange equations to transofrm the optimal control problem into a two-point boundary value problem (BVP). Conventionally these problems have been solved using the multiple shooting differential equation solver, or variants of it. In this work the …
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A hybrid method for flows in local chemical equilibrium and nonequilibrium
The primary objective of this work is to develop a more efficient chemically active compressible Euler equation solver. Currently, a choice between the physical accuracy of a finite-rate solver or the computational efficiency of an equilibrium flow solver must be made. The number of species modeled …
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Interplay of Geometry and Mechanics: Disordered Spring Networks and Shape-changing Cerebella
… develops a quadratic non-linearity in the Euler-Lagrange equations. We study the effect of such a non-linear force for a simple harmonic oscillator like system and see that there too we obtain cusped `folds'. We also discuss steric confinements on the growing cerebellum and a paradigmatic …
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Taming the Inverse and Forward Problems in Density Functional Theory
… Towards this end, the associated Euler-Lagrange equations, i.e. the Kohn-Sham equations, are often solved in practice, which demand a procedure that iterates an initial guess density to a \textit{self-consistent} density (the solution). A new framework is presented for evaluating the …
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Linear and non-linear deformations of a wind turbine blade considering warping and all aeroelastic load couplings
… vector (function of time step) of the dynamic equations of motion are deduced from the Lagrange equations of motion that were derived step by step. The steps of the linear and nonlinear Newmark implicit iteration schemes used for solving the linear and nonlinear dynamic equations of motion …
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Residual-based turbulence models for incompressible flows in domains with moving boundaries
… models are driven by the residual of the Euler-Lagrange equations for the coarse scales. Consequently, when the coarse scales are able to represent the exact solution of the problem, the fine-scale models vanish. Numerical attributes of the developed models are investigated via an exhaustive set …
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Vibration analysis and intelligent control of flexible rotor systems using smart materials
… bearing-induced axial force is modelled, the equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. In this thesis the axial force terms included in the equations of motion provide a means for axially …
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An analytical and experimental investigation of the response of elliptical composite cylinders
… analysis, based on Donnell’s nonlinear shell equations, is developed to study the prebuckling responses of geometrically perfect cylinders. In this analysis the circumferentially-varying radius of curvature of the cylinder is expanded in a cosine series. While elliptical sections are studied …
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A Long-Range Energy Model Aimed to Maximize Utility
Made available in DSpace on 2017-07-06T18:55:11Z (GMT). No. of bitstreams: 3 Luo_Jianding_MS.pdf: 38517059 bytes, checksum: f30acef3deccbd1e9315466a85aa4750 (MD5) Luo_Jianding_MS_ABS.pdf: 460590 bytes, checksum: d5edbdb7d9ed45d15af3ae6f01de992d (MD5) license.txt: 4813 bytes, checksum: …