Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

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Focusing on a global perspective in mechanics, this book introduces the variational formulation of Lagrangian and Hamiltonian dynamics. It presents a novel methodology to derive globally valid equations of motion on various types of configuration manifolds, such as Lie groups and homogeneous spaces. This approach effectively circumvents the challenges posed by coordinate singularities, offering a fresh conceptual framework that departs from traditional methods reliant on local coordinates.