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We construct Yang-Mills connections on SO(n)-bundles over spheres equippedwith the Euclidean metric. We use a cohomogeneity one group action on thebundle to reduce the Yang-Mills-equation to a system of ordinary differentialequations. The system is shown to have solutions by variational methods, usingideas from harmonic map theory. Examples include Yang-Mills connections on eachof the countably many principal SO(6)-bundles over $S^6$, and countably manyYang-Mills connections on $TS^n$ for $n\in\{5,...,9\}$.

Yang-Mills connections of cohomogeneity one on SO(n)-bundles over Euclidean spheres