The alternating forces on a piston cause its reciprocating motion. Combustion chamber pressure is one of those forces. The other principle force is from the connecting rod. These forces can be large. The YankeeDiesel double piston is larger yet. Therefore its changing momentum is big. The calculations below compare the forces need to compress that air and the force needed to reverse the double piston’s motion. Think of the piston as a flywheel. Does it have enough energy to compress the air?
The short answer is no.
It only has about a third of the energy needed. Therefore most of the power to compress the air comes from the companion. The companion piston is connected directly to it and some of its combustion power is used for its mate’s compression. YankeeDiesel has no connecting rods so there is no side load in transmitting this force. This also means that the crankshaft must transmit only the net power out of the engine. The power to compress the air charge is exchanged between piston pairs.