Analytical Mechanics

• 1 Basic definitions.- 2 Rigid body kinematics — basic knowledge.- 3 Theory of finite rotations of rigid bodies.- 4 Basic dynamic quantities.- 5 Work and potential energy.- 6 The fundamental equation of dynamics. Analytical statics.- 7 Lagrange’s differential equations.- 8 Other forms of differential equations of motion.- 9 Dynamics of relative motion.- 10 Canonical equations and Jacobi’s theorem.- 11 Perturbation theory.- 12 Variational principles in mechanics.- A Elements of the theory of matrices.- A.1 Definitions.- A.2 Operations on matrices.- A.3 Inverse of the matrix.- A.4 Matrix representation of the operations of vector calculus.- A.5 Differentiation of a matrix.- B Basics of tensor calculus.- B.1 General non-orthogonal coordinates.- B.2 Vectors using the non-orthogonal coordinates.- B.3 Tensors of second rank in the non-orthogonal coordinates.- B.4 Curvilinear coordinates.- B.5 Covariant differentiation.- B.6 Examples of non-orthogonal curvilinear coordinates.- B.7 Formulae ofthe theory of surfaces.- B.8 Curvature of lines on the surface.- B.9 Covariant derivative of a vector on the surface.- B.10 Orthogonal curvilinear coordinates.- B.11 Finite-dimensional Euclidean space.- B.14 The Riemann-Christoffel tensor.- References.

From the reviews: "This monumental treatise on analytical mechanics is a translation of the original Russian edition from 1961. ... it contains a wealth of material on the classic theory of mechanics, and methods of formulating the equations of motion of mechanical systems. ... This book ... makes good background reading for anyone with an interest in the classical foundations of mechanics. The gradual build up to the general equations and principles, supplemented with many examples, prepares the reader well ... ." (Steen Krenk, Journal of Vibration and Acoustics, April, 2004) "This book is a translation of a book originally printed in Russian in 1961. It offers a treatment of the dynamics of mechanical systems. ... Analytical Mechanics would be a useful reference book for a person who is interested in engineering dynamics. It could also serve as a textbook for a graduate course in engineering dynamics ... ." (Richard H. Rand, SIAM Review, Vol. 45 (2), 2003) "This textbook ... represents the lectures of a late great scholar and teacher at the Saint-Petersburg Polytechnic Institute. ... the work is of original conception and contains also original contributions of the author. ... A great attention is paid to the statement of problems and to the construction of the corresponding equations of motion. The book could be of interest to a large circle of graduate students as well as to researchers in the field who wish to acquire a deeper insight into analytical mechanics." (P. Teodorescu, Zentralblatt MATH, Vol. 1015, 2003)