Linearizing coordinate transformations and Riemann curvature

Using the Lagrangian framework and point transformations, an alternative derivation of an existing result on the special decomposition of the inertia matrix is presented. The Riemann curvature tensor is introduced as a computational tool to test for this special decomposition. An example with configuration-dependent inertia which admits such a factorization is presented. For the cart-pole problem, it is shown that such a decomposition is possible and the linearizing transformation is computed. It is shown that a planar two-link manipulator cannot be linearized by point transformations only