عنوان

Variational Methods and Complementary Formulations in Dynamics

9401582599

9789401582599

b591919

Variational Methods and Complementary Formulations in Dynamics

[Book]

by B. Tabarrok, F.P.J. Rimrott.

Dordrecht

Springer Netherlands

1994

(xii, 368 pages)

Solid mechanics and its applications, 31.

I --; Fundamentals --; II --; Differential Variational Formulations --; III --; Integral Variational Formulations --; IV --; Canonical Transformations and the Hamilton-Jacobi Equation --; V --; Rigid Body Dynamics --; VI --; Special Applications --; Appendix A --; The Calculus of Variations --; A.1 Functions and Functionals --; A.2 Review of Extremum Values of Functions --; A.3 Stationary Values of Definite Integrals --; A.4 A Note about Weak and Strong Variations --; A.5 An Alternative Expression for a Single Euler-Lagrange Equation --; A.6 The Brachystochrone Problem --; A.7 Path-independent Functionals --; A.8 Several Dependent Functions --; A.9 Variational Notation --; A.10 Constraint Equations --; Lagrange Multipliers --; Algebraic and Differential Equation Constraints --; A.11 Variable End Points --; Suggested Reading --; Appendix B --; Developments in Mechanics --; Some Historical Perspectives --; Author Index.

Variational methods provide a versatile framework for several branches of theoretical mechanics. For problems in dynamics, variational formulations provide a powerful alternative to vector methods. This approach has a rich legacy of ideas advanced by numerous researchers including such celebrated mathematicians as d'Alembert, Lagrange, Hamilton, Jacobi, Gauss and Euler. In this volume, the subject matter is developed systematically with many worked-out problems. Initially, differential variational formulations are described followed by the integral formulations. A detailed account of the essentials of the calculus of variations is provided. While classical formulations in dynamics have a long history, the complementary formulations are relatively new. This book is the first to provide a detailed development of complementary formulations and also highlights certain dualities that are revealed as a consequence of the two formulations. A chapter on special applications studies problems of small amplitude oscillations about equilibrium and steady state configurations, and the problem of impulsive or spike loads. The book ends with historical sketches of the personalities associated with variational methods in dynamics. For structural, mechanical and aeronautical engineers. This volume can also be recommended as a graduate text in analytic dynamics.

Engineering.

Mathematical optimization.

Mechanics.

by B. Tabarrok, F.P.J. Rimrott.

B Tabarrok

F P J Rimrott

[Book]

Y