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Euler‐Lagrange Equation in Free Coordinates
Journal of Mathematics, 2022 In this paper, we introduce different equivalent formulations of variational principle. The language of differential forms and manifold has been utilized to deduce Euler–Lagrange equations in free coordinates. Thus, the expression is simple and global.
Mastourah M. Alotaibi, Sami H. Altoum
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Fractional Euler-Lagrange Equations Applied to Oscillatory Systems
Mathematics, 2015 In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional nonlinear dynamic equations involving two classical physical applications: “Simple Pendulum” and the “Spring-Mass ...
Sergio Adriani David +1 more
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Frontiers in Physics, 2019 In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler–Lagrange equations of motion are ...
Amin Jajarmi +4 more
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Modelling and Simulation in Engineering, 2011 A computable model of grasping and manipulation of a 3D rigid object with arbitrary smooth surfaces by multiple robot fingers with smooth fingertip surfaces is derived under rolling contact constraints between surfaces.
Suguru Arimoto, Morio Yoshida
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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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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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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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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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Dynamical equations of multibody systems on Lie groups
Advances in Mechanical Engineering, 2015 The Euler–Poinaré principle is a reduced Hamilton’s principle under Lie group framework. In this article, it is applied to derive a hybrid set of dynamical equations of rigid multibody systems, which include four parts: the classical Euler–Lagrange ...
Wenjie Yu, Zhenkuan Pan
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Just-in-Time Optimal Routing in the Presence of Non-Uniform and Time-Evolving Uncertainty
Applied SciencesTrajectory planning aims to compute an optimal path and velocity of an agent through the minimization of a cost function. This paper proposes a just-in-time routing method, incorporating the stochastic minimization of a cost function, which ingests the ...
Chady Ghnatios, Francisco Chinesta
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