An unbalanced gyroscopic apparatus is disclosed for producing unidirectional thrust without having to interact with an external gas, liquid, or solid mass. The technique is based on the controlled transitions of an unbalanced spinning mass between two stable unbalanced weight states resulting in a net unidirectional thrust at the spin axis. In one existing embodiment, an apparatus with an attached body can be propelled up a planar incline “sliding” uphill against terrestrial gravity. In another embodiment, multiple pairs of synchronized and mirror-image, unbalanced gyroscopic assemblies are combined as one apparatus and attached to a body with the potential to propel it in any direction, including defeating gravity completely without interaction with gas, liquid, or solid mass or without use of propellants.