Tensor Calculus And Analytical Dynamics

Tensor Calculus and Analytical Dynamics provides a concise, yet comprehensive, and readable introduction to classical tensor calculus-in both holonomic and nonholonomic coordinates-and its principal applications to the Lagrangean analytical dynamics, i.e. the energetic mechanics of constrained systems with a finite number of degrees of freedom. Tensor Calculus and Analytical Dynamics, the only work of its kind in English, in or out of print, and among a handful in any language, contains accessible treatments of such intricate topics as : • Tensor calculus in nonholonomic variables, Pfaffian (possibly nonholonomic) constraints, and the integrability theorem of Frobenius • Most general principles and equations of motion of Lagrangean dynamics, from a simple unified viewpoint. Written for the theoretically-minded engineer, physicist, mathematician- in the best classical tradition of applied mathematics (e.g., Appell, Levi-Civita, Schouten, Veblen, Vranceanu), mechanics (e.g., Hamel, Synge, Lure), and physics, (e.g., Brillouin, Einstein, Eddington, Weyl)-the book enables its readers to move quickly and confidently into any particular geometry-based area of classical or modern theoretical dynamics. FEATURES • Avoids all unnecessary mathematical formalisms ("epsilonics "), thus making the work accessible to as many readers as possible • Employs indicial notation-which, unlike direct/matrix notations, combines both coordinate generality and coordinate specificity • Focuses on the basic geometrical/physical ideas and formal structure of the advanced dynamics of mechanical systems under general positional and/or velocity (Pfaffian) constraints, via the kinetic principle of virtual work • Contains many nontrivial, completely solved examples, as well as problems with answers and hints.