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Any sufficiently often differentiable curve in the orbit space V/G of a real finite-dimensional orthogonal representation G → O(V) of a finite group G admits a differentiable lift into the representation space V with locally bounded derivative. As a consequence any sufficiently often differentiable curve in the orbit space V/G can be lifted twice differentiably. These results can be generalized to arbitrary polar representations. Finite reflection groups and finite rotation groups in dimensions two and three are discussed in detail.arXiv:math/0504101v1 fatcat:ve5gbjor6nbh5p6krfi5vmjyka