Abstract
A new <inline-formula><tex-math notation="LaTeX">$\mathrm{S}^{1}$</tex-math></inline-formula> principal bundle over a vector space with the origin removed is constructed for the drone with the yaw dynamics evolving on the <inline-formula><tex-math notation="LaTeX">$\mathrm{S}^{1}$</tex-math></inline-formula> fiber and the remaining part of drone dynamics on the base space. Two local trivializations are constructed to cover the whole bundle such that on each trivialization the drone dynamics is transformed via dynamic feedback to a linear controllable system with the yaw dynamics decoupled from the rest of the drone dynamics to make easy the design of drone trajectories and controls. The manifold <inline-formula><tex-math notation="LaTeX">$\mathrm{S}^{2}$</tex-math></inline-formula> often used for thrust directions is made obsolete by the new bundle.
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