System of hydrodynamic type admitting two quadratic integrals of motion

A pneumatic braking system includes two first pneumatic braking circuits of a motor vehicle and a second pneumatic braking circuit of a trailer towed by the vehicle and which second braking circuit is to be controlled in dependence upon the operation of the first braking circuits. A control valve unit provides such control and has a housing an outlet of which communicates with the second circuit, and a chamber contains fluid at the pressure of a reservoir. A valve arrangement is displaceable between a first position in which it connects the outlet with the ambient atmosphere, a second position in which it disconnects the outlet from the ambient atmosphere, and a third position in which it connects the outlet with the aforementioned chamber to thereby pressurize the second circuit. A pair of first pistons are shiftable in the housing from a normal rest position to a operated position in response to pressurization of the first circuits during braking of the vehicle. A compound second piston controls the movements of the valve arrangement, and has one piston portion connected with the valve arrangement and shiftable in the housing to thereby displace the valve arrangement sequentially from the first to the second and then toward the third position in response to movement of at least one of the first pistons to the operated position thereof. The second piston also includes another piston portion which is biased away from the one piston portion and which has a surface communicating with the interior of the outlet so that when the second circuit is partially pressurized during movement of the valve arrangement from the second towards the third position and pressure in the outlet exceeds the biasing force, the other piston portion will move into abutment with the one piston portion to thereby slow the shifting of the same and the displacement of the valve arrangement towards the third position thereof.