Applied Differential Geometry: A Modern Introduction
This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the worldOCOs leading human motion simulator OCo OC Human Biodynamics EngineOCO, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools OCo this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models."
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Abelian action adjoint affine biodynamical c—split called canonical classical cohomology commutative compact complex components connection consider coordinates corresponding cotangent bundle covariant curvature curve defined denote diagram diffeomorphism differential dimension dual dynamical equation equivalent Euclidean example exterior fiber fibre bundle field theory finite formula function functor gauge theory geodesic geometrical given group G Hamiltonian bundle Hamiltonian form homomorphism homotopy identity integral invariant isomorphism Ivancevic Kahler Lagrangian Lie algebra Lie bracket Lie derivative Lie group linear loop matrix mechanics metric tensor moduli space morphism nonlinear objects operator parameter particle phase-space physical quantum gravity Recall relation representation represents resp respect Riemannian manifold Riemannian metric Sardanashvily scalar smooth manifold solution space-time string theory structure submanifold supersymmetry symmetry symplectic manifold tangent bundle tensor-field Theorem topological space transformation trivial vector bundle vector space vector-field velocity