The analogue of the Chaplygin sleigh is the torpedo. Now, the body glides frictionlessly through space rather than the plane. 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. This system is the natural analogue to the Chaplygin sleigh since it lives in SE 3 ( R ) ≅ ≅ SO ( 3 ) ⋊ ⋊ R 3 .