General properties of the Casimir force are reviewed, with particular attention to the effects of geometry. Using the conservation of energy, the forces in several simple idealized structures are derived, including the lateral forces on partially overlapping parallel plates, the force in a Casimir “comb” drive with several interleaved surfaces, and the average force when a plate is inserted into a rectangular cavity. The properties of rectangular cavities with a moveable piston are discussed, and illustrated with numerical computations. An oscillating structure is proposed.

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