### Relational Mechanics as a gauge theory: Machianization and dragging effect in galactic halos

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The elimination of absolute space from the body of mechanics is achieved by gauging translations and rotations in the kinetic energy of an isolated system. As a result, the gauge invariant Lagrangian leads to equations of motion that can be used in any frame. Nevertheless, there are privileged frames where Newton’s equations are valid, but they are determined by the matter distribution of the universe (Machianization). The relational equations of motion shows that there exists a dragging effect in galactic halos that contributes to the rotation curves. On the other hand, the absence of an absolute time is characteristic of parametrized systems, which are systems possessing an internal time. Parametrized systems with potentials that are proportional to inverse square distances are as well gauge invariant under scalings (shape-dynamics).