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The Mathematical Gazette, 1935
Students find partial differential equations difficult not only on account of the inherent difficulties of the subject, but because of confusion, omissions, and, frequently, errors in the textbooks. To take an illustration, Piaggio (p. 147, new edition), begins with the statement that the equations
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Students find partial differential equations difficult not only on account of the inherent difficulties of the subject, but because of confusion, omissions, and, frequently, errors in the textbooks. To take an illustration, Piaggio (p. 147, new edition), begins with the statement that the equations
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Fractional Euler–Lagrange equations revisited
Nonlinear Dynamics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Herzallah, Mohamed A. E. +1 more
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Russian Mathematics, 2015
In this paper, we proceed with studying matrix equations over “skew series”. We establish conditions for splitting a Lagrange matrix equation into a set of scalar differential equations. We consider diagonal, triangular, nil-triangular, and dual-diagonal forms of its solution.
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In this paper, we proceed with studying matrix equations over “skew series”. We establish conditions for splitting a Lagrange matrix equation into a set of scalar differential equations. We consider diagonal, triangular, nil-triangular, and dual-diagonal forms of its solution.
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Electret transducer equations by Lagrange’s equation
The Journal of the Acoustical Society of America, 1978The equations of motion of the electret foil transducer are derived by applying Lagrange’s equation to the total electrical and mechanical energies of the transducer system. The resulting equations apply for the operation of the transducer both as a sound source and as a sound pickup.
Melville S. Hawley, Frank F. Romanow
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1977
The fundamental equation in generalized coordinates has been found in (12.3.9) as $$\sum\limits_{s = 1}^n {\left( {\frac{d}{{dt}}\frac{{\partial T}}{{\partial \dot q_s }} - \frac{{\partial T}}{{\partial q_s }} - Q_s } \right)\delta q_s = 0,}$$ (13.1.1) where the kinetic energy T and the generalized forces Q s are, in general, functions of all
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The fundamental equation in generalized coordinates has been found in (12.3.9) as $$\sum\limits_{s = 1}^n {\left( {\frac{d}{{dt}}\frac{{\partial T}}{{\partial \dot q_s }} - \frac{{\partial T}}{{\partial q_s }} - Q_s } \right)\delta q_s = 0,}$$ (13.1.1) where the kinetic energy T and the generalized forces Q s are, in general, functions of all
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Lagrange’s differential equations
2002Differential equations of motion for the generalised coordinates can be obtained easily with the help of Lagrange’s central equation. The equations will be derived twice here. The first derivation will assume that the operations d and δ are not interchangeable, while the second one will assume that the operations are interchangeable. In the first case,
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2015
Abstract. In this paper we examine the Euler- Lagrange equation and by expressing the fundamental thermo of calculus of variations, we calculate the Euler- Lagrange equation for the simplest problem of calculus of variations and by offering an example we will discuss the specific modes of Euler - Lagrange equation.
FATHI POOR, Zahra +2 more
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Abstract. In this paper we examine the Euler- Lagrange equation and by expressing the fundamental thermo of calculus of variations, we calculate the Euler- Lagrange equation for the simplest problem of calculus of variations and by offering an example we will discuss the specific modes of Euler - Lagrange equation.
FATHI POOR, Zahra +2 more
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2010
Let \(\{\mathcal{M};d\mu \}\)be a material system whose mechanical state is described by N Lagrangian coordinates \(q = ({q}_{1},\ldots, {q}_{N})\). Since every point \(P \in \{\mathcal{M};d\mu \}\)is identified along its motion by the map (q, t) → P(q, t), the configuration of the system is determined, instant by instant, by the map \(t \rightarrow q ...
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Let \(\{\mathcal{M};d\mu \}\)be a material system whose mechanical state is described by N Lagrangian coordinates \(q = ({q}_{1},\ldots, {q}_{N})\). Since every point \(P \in \{\mathcal{M};d\mu \}\)is identified along its motion by the map (q, t) → P(q, t), the configuration of the system is determined, instant by instant, by the map \(t \rightarrow q ...
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LAGRANGE Equations of Second Kind
1970The LAGRANGE-equation s of the 2nd kind are very well known. Therefore, only a special question will be illustrated by an example.
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