Euler’s equation
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Part 1 of ebook "Theory and design of charged particle beams" provides readers with contents including: Chapter 1 - Introduction; Chapter 2 - Review of charged particle dynamics; Chapter 3 - Beam optics and focusing systems without space charge; Chapter 4 - Linear beam optics with space charge;...
326p giangdongdinh 28-05-2024 3 2 Download
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The paper "Nonlinear vibration of functionally graded porous micro-beams resting on elastic foundation" presents the analysis of nonlinear vibration of functionally graded porous (FGP) micro-beams resting on an elastic foundation. The Euler-Bernoulli beam theory (EBT) and the nonlocal strain gradient theory (NSGT) are considered to establish the equations of motion of the micro-beam. The material properties of the micro-beam are assumed to be changed continuously along thickness direction according to simple power-law distribution.
9p dathienlang1012 03-05-2024 1 0 Download
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Ebook "Physical oceanography: A mathematical introduction with matlab®" is about the interplay between applied mathematics and the field of geophysical fluid dynamics. Its primary goals are to demonstrate how one uses the basic tenets of multivariate calculus to derive the governing equations of fluid dynamics in a rotating frame, and how one uses methods from linear algebra and partial differential equations to solve some of the basic initial-boundary value problems that have become the hallmark of physical oceanography.
454p duongthandue0501 28-02-2024 2 1 Download
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Part 1 of ebook "Physics from symmetry" provides readers with contents including: foundations; symmetry tools; special relativity; lie group theory; the framework; elementary particles and fundamental forces; lorentz transformations; representation theory; euler-lagrange equation;...
130p dangsovu 20-10-2023 9 3 Download
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In this paper, we introduce a tamed-adaptive Euler-Maruyama approximation scheme for stochastic differential equations with Markovian switching. We show that the scheme converges in L 1 -norm when applying for SDEs with locally Lipschitz continuous drift and locally Holder continuous diffusion.
21p visharma 20-10-2023 6 2 Download
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In particular, the drift coefficient blows up at 0. We first prove that this equation has a unique positive solution, and then propose a semi-implicit Euler approximation scheme for the equation, and finally show that it is also positive, and study its rate of convergence.
14p viberkshire 09-08-2023 6 3 Download
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Continued part 1, part 2 of ebook "Classical mechanics with calculus of variations and optimal control: An intuitive introduction" provides readers with content including: Chapter 4 - Variational principles of mechanics; Chapter 5 - Classical problems of calculus of variations; Chapter 6 - The conditions of legendre and jacobi for a minimum; Chapter 7 - Optimal control; Chapter 8 - Heuristic foundations of hamiltonian mechanics;...
135p dieptieuung 19-07-2023 3 3 Download
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The size-dependent behavior of a silicon microbeam with an axial force in MEMS is studied using a nonlinear finite element procedure. Based on a refined thirdorder shear deformation theory and the modified couple stress theory (MCST), nonlinear differential equations of motion for the beam are derived from Hamilton’s principle, and they are transferred to a discretized form using a two-node beam element.
13p viwolverine 11-07-2023 3 2 Download
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The paper proposed a balancing control for MIMO under-actuated systems. In this paper, human walking robots, the athlete robot, are researched. The dynamic equations of this model are generated by Euler Lagrange method.
9p vidoctorstrange 06-05-2023 4 1 Download
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Most kinds of robots in researches are in solid structures. In these models, Euler-Lagrange method is easily used to obtain dynamic equations for simulation and obtaining controllers. But, actually, there is always flexibility - even very small or remarkable – in all kinds of robots. This research solves a problem in modelling a complex robot with a flexible link-flexible inverted pendulum- by presenting a method to simplify that robot.
8p vidoctorstrange 06-05-2023 6 4 Download
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In the paper, the forced transverse vibration of fractional viscoelastic Euler-Bernoulli is studied. Based on the fractional relationship of stress and strain, the partial differential equation describing transverse vibration of Euler-Bernoulli viscoelastic beam is considered.
13p vidudley 20-02-2023 6 2 Download
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Free vibration of functionally graded beams resting on winkler foundation around the buckling domain
This paper investigates free vibration of functionally graded beams (FG beams) resting on Winkler foundation around the buckling domain. The governing equations of motion based on Euler–Bernoulli and Timoshenko beam theories together with Von Karman’s strain–displacement relation are derived from Lagrange’s equations.
6p vispyker 16-11-2022 5 1 Download
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This paper establishes a dynamic model of tractor semitrailer vehicle, based on Multi-Body System Method analysis and Newton-Euler equations with Burckhardt’s tire model. This model is applied to evaluate the effect of road conditions on lateral instability of the tractor semitrailer vehicle during turning maneuver.
7p viporsche 25-10-2022 6 3 Download
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In this paper, a full dynamic model of tractor semitrailer is developed based on Multi-body System Method and Newton-Euler equations. The rollover condition is based on the load transfer ratio which corresponds to the load transfer between the left and the right sides of the vehicle.
5p vimelindagates 18-07-2022 6 4 Download
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This paper focuses on building a theoretical method, based on the calculation of hydraulic losses to predict the energy performance of a Low-specific speed Pump as Turbine (PaT) quickly and accurately that supported for the PaT’s impeller design. The Euler equation is built with the analysis of hydraulic loss calculation and flow phenomena passing on the machine.
7p vimelindagates 18-07-2022 5 2 Download
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This paper presents a method to synthesize the adaptive sliding mode controller for a class of MIMO Euler-Lagarance systems with variable parameters. We perform a Taylor series expansion of a class of MIMO Euler-Lagarance systems into nonlinear state-space equations, considering cases of varying parameters and unmeasured external disturbances.
9p viirenerosenfeld 26-05-2022 17 2 Download
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This study attempts to develop a numerical scheme for 2-D transient analysis under unsaturated conditions. First, the unsaturated groundwater flow was described using the mass conservation law. Then, the Finite Difference Method and Backward Euler approximation were applied for space and time discretization, respectively.
11p haoasakura 30-05-2022 9 1 Download
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The presented models are more generalized in terms of damping, in-plane vibration, and asymmetry. The equations of motion for a 2DOF case that are compact enough are presented. It is shown that asymmetric coefficients of kinetic friction may have stabilizing effect while softening the tangential pads’ supports can either stabilize or destabilize the trivial solution of the system.
11p spiritedaway36 25-11-2021 17 1 Download
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The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler–Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution.
23p nguaconbaynhay11 07-04-2021 19 2 Download
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The dynamic response to variable magnitude moving distributed masses of simply supported non-uniform Bernoulli–Euler beam resting on Pasternak elastic foundation is investigated in this paper. The problem is governed by fourth order partial differential equation with variable and singular coefficients. The main objective of this work is to obtain closed form solution to this class of dynamical problem.
16p nguaconbaynhay11 07-04-2021 7 1 Download