A damping device intended to be mounted on a vehicle 12, comprising a housing (4) resting on first (6) and second (8) support members arranged at a longitudinal distance apart from one another, the housing being capable of displacement relative to the support members (6, 8) in accordance with a transverse movement and a pivoting movement about a point (46) situated substantially on a medium longitudinal axis of the vehicle (2) and between the support members, said device comprising:
- first (10) and second (10′) symmetrical jacks, extending respectively between each support member (8, 6) and the housing (4), each jack (10, 10′) defining first (24, 24′) and second (26, 26′) chambers filled with a hydraulic fluid (16, 16′) capable of being, respectively, compressed and let down during variations in the transverse distance between the housing (4) and each support member (6, 8),
- a first (28) hydraulic line establishing fluid communication between the first chambers (24, 24′) of the first (10) and second (10′) jacks, and a second hydraulic line (28′) establishing fluid communication between the second chambers (26, 26′) of the first (10) and second (10′) jacks, said first (28) and second (28′) lines respectively possessing first (29) and second (29′) intermediate points from which extend first (30) and second (30′) branch lines opening, opposite the intermediate points, into first (32) and second (32′) accumulators containing a compressed gas,
- first to fourth means (34, 35, 40, 42) for controlling the flow of the hydraulic fluid, arranged between each of the chambers (24, 24′, 26, 26′) and one of the intermediate points (29, 29′) and capable of providing a controlled flow rate of the fluid from the chambers to the intermediate points, and
- fifth and sixth means (38, 44) for controlling the flow of the hydraulic fluid, arranged between each of the intermediate points (29, 29′) and the corresponding accumulator (32, 32′) and capable of providing a controlled flow rate of the fluid from the intermediate points to the accumulators,
- the chambers (24, 24′, 26, 26′) between which communication is established by each of the two lines (28, 28′) being respectively let down and compressed during a first type of movement between the support members (6, 8) and the housing (4), so that substantially all of the fluid driven from each compressed chamber (24′, 26) penetrates into the let-down chamber (24, 26′) with which it communicates, generally without any variation in the volume of fluid in the accumulators (32, 32′), and
- the chambers (24, 24′) communicating via one (28) of the lines both being compressed during a second type of movement between the support members (6, 8) and the housing (4), so as to direct the fluid driven from these two compressed chambers (24, 24′) to one of the accumulators (32) and to increase the pressure of the gas contained therein, while the chambers (26, 26′) communicating via the other (28′) of the lines are both let down, so as to direct to these two let-down chambers (26, 26′) part of the fluid present in the other accumulator (32′) and to reduce the pressure of the gas contained therein.