Control theory plays a fundamental role in the modeling and trajectory planning of actuated dynamical systems. In recent decades, the use of differential geometric methods, namely Lagrangian and Hamiltonian mechanics, has become prevalent within the control theory literature due to the...

It is well known that the collection of linear frames of a smooth n-manifold M defines a principal GL(n, R)-bundle over M (called the frame bundle); more generally, this construction makes sense for any vector bundle over M. Conversely, any principal bundle together with a representation...

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