Presents a general first-order kinematic model of frictionless rigid-body contact for use in hybrid force/motion control. It is formulated in an invariant manner by treating motion and force vectors as members of two separate but dual vector spaces. These more general kinematics allow us to model tasks that cannot be described using the Raibert-Craig model; a single Cartesian frame in which directions are either force- or motion-controlled is not sufficient. The model can be integrated with the object and manipulator dynamics in order to model both the kinematics and dynamics of contact. These equations of motion can be used to design force and motion controllers in the appropriate subspaces. To guarantee decoupling between the controllers, it is possible to apply projection matrices to the controller outputs that depend solely on the kinematic model of contact, not a dynamic one. Experimental results show a manipulation that involves controlling the force in two separate face-vertex contacts while performing motion. These multi-contact compliant motions often occur as part of an assembly and cannot be described using the Raibert-Craig model.