The motion is attracted to an equilibrium, in which the sleigh moves without rotation, with the knife edge trailing the center of mass.
Let v be the velocity, with positive values indicating that the knife edge trails.
The equations of motion are symmetric under time reversal, but asymmetric under inversion of the body-fixed axis aligned with the knife edge.
In geometric mechanics, the Chaplygin sleigh lives in the special Euclidean group
The system is constrained to slide only longitudinally and cannot twist around the direction of motion similar to how a torpedo moves through water.
The dimension of the phase space is 9 since there are 6 positions and 6 velocities coupled with 3 constraints.