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.
