Variational Methods and Complementary Formulations in Dynamics

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 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 worked-out problems. Initially, differential variational formulations are described followed by the integral formulations. An 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 aims to provide a detailed development of complementary formulations and highlight certain dualities that are revealed as a consequence of the two formulations. The 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. Designed for structural, mechanical and aeronautical engineers, this volume should also be useful as a graduate text in analytic dynamics.