An engine includes a first piston with surfaces that define a substantially cylindrical chamber inside the first piston and a passage into the substantially cylindrical chamber. One or more second pistons are arranged to reciprocate inside the substantially cylindrical chamber and to define, in cooperation with the substantially cylindrical chamber, a combustion chamber. A fuel injector extends at least partially through the passage in the first piston to inject fuel into the combustion chamber. The first piston is arranged to move in a reciprocating manner relative to the fuel injector.