The invention relates to an aircraft undercarriage comprising: a strut (1) for connecting to the aircraft, a slide rod (3) slidably engaged in leaktight manner in the strut via the bottom opening, which rod carries at least one wheel at its bottom end, a diaphragm (7) carried by a support (8) attached to the top wall of the strut to cooperate in leaktight manner with an inside wall of the slide rod so as to define a first chamber (C1) under the diaphragm inside the rod and completely filled with hydraulic fluid, and a second chamber (C2) above the diaphragm and partially filled with hydraulic fluid, a throttle needle (10) secured to the slide rod and penetrating into a calibrated orifice (12) in the diaphragm so as to define a calibrated fluid passage between the first and second chambers, and angular connection means for imposing an angular position on the slide rod relative to the strut. According to the invention, the undercarriage includes at least one vane (20) fastened to the end of the throttle needle in order to extend inside a portion of the second chamber that is filled with hydraulic fluid.