Differential Geometry offers a concise introduction to some basic
notions of modern differential geometry and their applications to solid
mechanics and physics.
Concepts such as manifolds, groups, fibre bundles and groupoids are
first introduced within a purely topological framework. They are shown
to be relevant to the description of space-time, configuration spaces of
mechanical systems, symmetries in general, microstructure and local and
distant symmetries of the constitutive response of continuous media.
Once these ideas have been grasped at the topological level, the
differential structure needed for the description of physical fields is
introduced in terms of differentiable manifolds and principal frame
bundles. These mathematical concepts are then illustrated with examples
from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy
fluxes and dislocation theory.
This book will be useful for researchers and graduate students in
science and engineering.