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Hamilton's principle
About: Hamilton's principle is a research topic. Over the lifetime, 2447 publications have been published within this topic receiving 46861 citations.
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Book•
01 Jan 1965
TL;DR: In this paper, the Calculus of Variation is used to describe the dynamics of a system of Particles and their motion in a noninertial reference frame, including central-force motion and coupling oscillations.
Abstract: Matrices, Vectors, and Vector Calculus. Newtonian Mechanics: Single Particle. Oscillations. Nonlinear Oscillations and Chaos. Gravitation. Some Methods in the Calculus of Variation. Hamilton's Principle: Lagrangian and Hamilton's Dynamics. Central-Force Motion. Dynamics of a System of Particles. Motion in a Noninertial Reference Frame. Dynamics of Rigid Bodies. Coupled Oscillations. Continuous Systems: Waves. The Special Theory of Relativity.
1,221 citations
Book•
01 Jan 2002
TL;DR: In this paper, the authors present a review of the work, energy, and variational calculus of solid mechanics and their application in the analysis of plate models. But their focus is on the theory and analysis of plates.
Abstract: Preface xv 1 Introduction 1 2 Mathematical Preliminaries 8 3 Review Of Equations Of Solid Mechanics 48 4 Work, Energy, And Variational Calculus 79 5 Energy Principles Of Structural 133 6 Dynamical Systems: Hamilton's Principle 177 7 Direct Variational Methods 204 8 Theory And Analysis Of Plates 299 9 The Finite Element Method 433 10 Mixed Variational Formulations 502 Answers / Solutions to Selected Problems 544 Index 583 About the Author 591
926 citations
TL;DR: In this article, an elementary but rigorous derivation for a variational principle for guiding center motion is given, and the application of variational principles in the derivation and solution of gyrokinetic equations is discussed.
Abstract: An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.
647 citations
TL;DR: In this paper, the full set of equations of motion for the classical water wave problem in Eulerian co-ordinates is obtained from a Lagrangian function which equals the pressure.
Abstract: The full set of equations of motion for the classical water wave problem in Eulerian co-ordinates is obtained from a Lagrangian function which equals the pressure. This Lagrangian is compared with the more usual expression formed from kinetic minus potential energy.
520 citations