Tensor Calculus and Analytical Dynamics

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Tensor Calculus and Analytical Dynamics provides a concise, but comprehensive, introduction to classical tensor calculus in both holonomic and nonholonomic coordinates as well as to its principal applications to the Lagrangean analytical dynamics of discrete and constrained systems. 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 mathematician, the book contains: a unique chapter on tensor calculus in nonholonomic variables, accessible discussion of Pfaffian nonholonomic constraints and the integrability theories of Frobenius, unified treatment of Lagrangean (constrained) dynamics . The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical dynamics in either classical or modern form. TOC:Tensor Calculus: Introduction and Background.- Tensor Algebra.- Tensor Analysis.- Analytical Dynamics: Introduction to Analytical Dynamics.- Particle on a Curve and on a Surface.- Lagrangean Mechanics: Kinematics.- Lagrangean Mechanics: Kinetics.