Results 291 to 300 of about 7,875,654 (350)

A variational principle for the equations of viscopiezoelectricity

IEEE Ultrasonics Symposium, 2004, 2005
The three-dimensional equations of linear viscopiezoelectricity and an accompanying electromechanical energy theorem are deduced, by the quasielectrostatic approximation, from the equations of viscoelectromagnetism and a generalized Poynting's theorem, respectively. For a viscopiezoelectric solid of volume V and bounding surface S, the internal energy,
Peter C Y, Lee, Nicholas P, Edwards
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Variational Solution of Integral Equations

IEEE Transactions on Microwave Theory and Techniques, 1974
A variational solution of the Fredholm integral equation of the first kind resulting from Laplace's equation with Dirichlet boundary conditions is discussed. Positive-definiteness of the integral operator is used to guarantee convergence. The square parallel plate capacitor is given as an example with several different types of trial functions. Special
McDonald, Bruce H., Friedman, Menahem, Wexler, Alvin   +2 more
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Constants of motion and the variational equations

Physical Review Letters, 1985
For field equations of Hamiltonian form the relation between constants of motion and solutions of the linearized equation is discussed. A known result is that the Poisson bracket of a constant of motion with the field variable solves the linearized equation.
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A variational approach to Liouville equations

Bollettino dell'Unione Matematica Italiana, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Sensitivity Equations and Variational Equations

1987
We assume an undisturbed state q i 0 , which satisfies the relationship (1.2.1) in a general phase space R n . The system of first-order differential equations q i = F i which correspond to a mechanical system and are basic to Eqs. (1.2.1), can, for example, be given by the set of canonical Hamilton differential equa­tions.
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VECTOR FIELDS, VARIATIONAL EQUATIONS AND COMMUTATORS

International Journal of Bifurcation and Chaos, 2012
We study autonomous systems of first order ordinary differential equations, their corresponding vector fields and the autonomous system corresponding to the vector field of the commutator of two such autonomous systems. These vector fields form a Lie algebra.
Willi-Hans Steeb, Yorick Hardy, Igor Tanski   +2 more
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Lagrange multiplier and variational equations in mechanics

Journal of Engineering Mathematics, 2023
R. Nzengwa
semanticscholar   +1 more source

Quasi-variational equation

Mathematical Inequalities & Applications, 2004
Summary: The main result proved in this article is the following. There is an \(\overline{x}\in X\) such that \[ g(\overline{x})\in C(\overline{x})\;\text{and}\;\sup_{y\in C(\overline{x})} \Psi(\overline{x}, y)=\Psi(\overline{x}, g(\overline{x}))\] where \(C: X\to 2^Y\) is a correspondence (\(g\) is a function defined over \(X\) in \(Y\)) and a ...
Nessah, Rabia, Chu, Chengbin
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Variational Principle for Eigenvalue Equations

Journal of Mathematical Physics, 1967
A variational principle is developed to provide an estimate of an arbitrary functional of the eigen-functions of a set of eigenvalue equations. It is shown that the variational formalism is equivalent to a functional Taylor series expansion of the desired functional about the trial functions.
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Variational Equations and Inequalities

2012
In this chapter we review some standard results for boundary value and initial–boundary value problems, paying particular attention to weak or variational formulations. The first section will be concerned with elliptic variational equations, and this will be followed by a review of some material on elliptic variational inequalities.
Weimin Han, B. Daya Reddy
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