Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints.
Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as:
tensor calculus in nonholonomic variables
Pfaffian nonholonomic constraints
related integrability theory of Frobenius
The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.
Table of Contents
Introduction and Background
Introduction to Analytical Dynamics
Particle on a Curve and on a Surface
Lagrangean Mechanics: Kinematics
Lagrangean Mechanics: Kinetics
"This is a deep and complete work…in view of the fact that very few books in tensor analysis have appeared recently, the present monograph is one of the most up to date…highly recommended…"
-L.Y. Bahar in Applied Mechanics Review, September 1999
"The book is very carefully written and published, it should find many readers and young scientists who want to follow the beautiful Analytical Dynamics in research and teaching."
-Professor Peter MaiBer Applied Mechanics Review,September 1999
"The material covered in the book is certainly of a high interest in spite of the long tradition accumulated in the past and a considerable number of textbooks published... the book is intended to be a concise introductory tool to theoretical dynamics and aims to provide the reader with a strong background on the geometrical concepts supporting the formulation of the general equations of motion of constrained mechanical systems... Papastavridis achieves his purpose in handing down a coherent and understandable presentation inclusive of some solved examples and problems... The volume represents a valuable contribution to the dissemination of knowledge in the field of theoretical mechanics and may be recommended for graduate students and researchers in engineering, physics, and applied mathematics."
-Meccanica, vol. 35, #5, 2001