Global projections for variational nonsmooth mechanics

This paper improves the projected Hamilton's principle (PHP) formulation of nonsmooth mechanics. Central to the PHP is the use of a projection mapping, defined on the configuration space, to capture nonsmooth behaviors. To support applications of the PHP with multiple impact times and locations, we define mild topological assumptions under which nonsmooth mechanical systems can be transformed to a prescribed normal form. In normal form coordinates, we provide a globally valid projection for use in the PHP. For systems that do not permit the transformation to normal form, we examine the use of constrained coordinates and incorporate holonomic constraints into the PHP. Lastly, as a preview of future developments of the PHP, we discuss the application of the method on compact manifolds.