Analytical Dynamics: Theory and Applications

ISBN-13: 9780306486814 / Angielski / Twarda / 2004 / 340 str.

Mark D. Ardema; M. D. Ardema

Opis

In his great work, Mecanique Analytique (1788)- DEGREESLagrange used the term "analytical" to mean "non-geometrical." Indeed, Lagrange made the following boast: "No diagrams will be found in this work. The methods that I explain in it require neither constructions nor geometrical or mechanical arguments, but only the algebraic operations inherent to a regular and uniform process. Those who love Analysis will, with joy, see mechanics become a new branch of it and will be grateful to me for thus having extended its field." This was in marked contrast to Newton's Philosohiae Naturalis Principia Mathematica (1687) which is full of elaborate geometrical constructions. It has been remarked that the classical Greeks would have understood some of the Principia but none of the Mecanique Analytique. The term analytical dynamics has now come to mean the develop ments in dynamics from just after Newton to just before the advent of relativity theory and quantum mechanics, and it is this meaning of the term that is meant here. Frequent use will be made of diagrams to illus trate the theory and its applications, although it will be noted that as the book progresses and the material gets "more analytical," the number of figures per chapter tends to decrease, although not monotonicall

Recenzje

From the reviews of the first edition:

"The book takes a classical approach to the development of the methods of analytical dynamics. ... the book contains a large number of examples ... and most of them are quite instructive. Many examples are worked out in full detail in the text, and an even greater number of additional examples is given in the form of problems (without solutions). ... People who teach mechanics courses may find this collection of examples quite useful." (Volker Perlick, Zentralblatt MATH, Vol. 1087 (13), 2006)

Spis treści

Review of Newtonian Dynamics.- Motion and Constraints.- Virtual Displacement and Virtual Work.- Variational Principles.- Generalized Coordinates.- Lagrange’s Equations.- Formulation of Equations.- Integration of Equations.- Examples.- Central Force Motion.- Gyroscopic Motion.- Stability Of Motion.- Impulsive Motion.- Gibbs-Appell Equations.- Hamilton’s Equations.- Contact Transformations.- Hamilton-Jacobi Equation.- Approximation Methods.