Results 51 to 60 of about 4,851,792 (234)
Numerical aspects of two coupled harmonic oscillators
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 In this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system.
Asad Jihad, Florea Olivia
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Existence of a weak solution for fractional Euler-Lagrange equations [PDF]
, 2012 In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $$ \dfrac{\partial L}{\partial x} (u,D^\alpha_- u,t) + D^\alpha_+ (\dfrac{\partial L}{\
L. Bourdin
semanticscholar +1 more source
Necessary optimality conditions for fractional action-like problems with intrinsic and observer times [PDF]
, 2008 We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems.
Frederico, G.S.F., Torres, D.F.M.
core +1 more source
A Perspective on Interactive Theorem Provers in Physics
Advanced Science, EarlyView.Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley +1 more source
AxiomsThis paper presents an analysis of the Hamiltonian formulation for continuous systems with second-order derivatives derived from Dirac’s theory. This approach offers a unique perspective on the equations of motion compared to the traditional Euler ...
Yazen M. Alawaideh +5 more
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Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.It is a fact that slippage causes tracking errors in both longitudinal and lateral directions which results to have less travel distance in tracking a reference trajectory. Less travel distance means having energy loss of the battery and carrying loads less than planned.
Gokhan Bayar +2 more
wiley +1 more source
Advances in Mechanical Engineering, 2019 The implicit methods on Lie group are developed for multibody system dynamics. To avoid the violation of the displacement, velocity and acceleration constraints of the nonlinear differential-algebraic equations, the constraint-stabilized equations on Lie
Jieyu Ding, Zhenkuan Pan, Wei Zhang
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Beyond Furnaces: Harnessing In Situ Joule Heating for Efficient C1 Catalysis
Carbon Energy, EarlyView.Joule‐heated catalysis directly converts electrical energy into localized heat within conductive catalysts, overcoming the heat‐transfer limitations of conventional furnaces. This review summarizes recent advances in C1 molecule conversion, including CO2 methanation, reforming for hydrogen production, and HCHO/CO oxidation, while highlighting ...
Xue Kong +8 more
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RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem
Mathematics, 2022 In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an ...
Andrea Ossicini
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Front Propagation Through a Perforated Wall
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We consider a bistable reaction– diffusion equation ut=Δu+f(u)$u_t=\Delta u +f(u)$ on RN${\mathbb {R}}^N$ in the presence of an obstacle K$K$, which is a wall of infinite span with many holes. More precisely, K$K$ is a closed subset of RN${\mathbb {R}}^N$ with smooth boundary such that its projection onto the x1$x_1$‐axis is bounded and that ...
Henri Berestycki +2 more
wiley +1 more source