This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

This undergraduate textbook offers a unique introduction to steady flight and performance for fixed-wing aircraft from a twenty-first-century flight systems perspective. Emphasizing the interplay between mathematics and engineering, it fully explains the fundamentals of aircraft flight and develops the basic algebraic equations needed to obtain the conditions for gliding flight, level flight, climbing and descending flight, and turning flight. It covers every aspect of flight performance, including maximum and minimum air speed, maximum climb rate, minimum turn radius, flight ceiling, maximum range, and maximum endurance.

"Steady Aircraft Flight and Performance" features in-depth case studies of an executive jet and a general aviation propeller-driven aircraft, and uses MATLAB to compute and illustrate numerous flight performance measures and flight envelopes for each. Requiring only sophomore-level calculus and physics, it also includes a section on translational flight dynamics that makes a clear connection between steady flight and flight dynamics, thereby providing a bridge to further study.Offers the best introduction to steady aircraft flight and performance Provides a comprehensive treatment of the full range of steady flight conditions Covers steady flight performance and flight envelopes, including maximum and minimum air speed, maximum climb rate, minimum turn radius, and flight ceiling Uses mathematics and engineering to explain aircraft flight Features case studies of actual aircraft, illustrated using MATLAB Seamlessly bridges steady flight and translational flight dynamics