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Analytical Dynamics: Theory and Applications de Mark D. Ardema

Analytical Dynamics: Theory and Applications

Autor Mark D. Ardema
en Limba Engleză Hardback – 15 noi 2004
This book takes a traditional approach to the development of the methods of analytical dynamics, using two types of examples throughout: simple illustrations of key results and thorough applications to complex, real-life problems.
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Specificații

ISBN-13: 9780306486814
ISBN-10: 0306486814
Pagini: 340
Ilustrații: XVI, 340 p.
Dimensiuni: 178 x 254 x 18 mm
Greutate: 0.79 kg
Ediția:2005
Editura: Springer Us
Colecția Springer
Locul publicării:New York, NY, United States

Public țintă

Professional/practitioner

Descriere

In his great work, Mecanique Analytique (1788)-^Lagrange 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 monotonically.

Cuprins

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.

Recenzii

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)

Caracteristici

Includes supplementary material: sn.pub/extras