John G. (Georgia Institute of Technology, Atlanta, Georgia, USA) Papastavridis 
Tensor Calculus and Analytical Dynamics [PDF ebook] 

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: