A three-dimensional reachable set for a nonlinear controlled object ``Dubins car'' is investigated. The control is the angular velocity of rotation of the linear velocity vector. The control action is constrained by an integral quadratic constraint. Based on the Pontryagin maximum principle, a description of the motions generating the boundary of the reachable set is given. The motions leading to the boundary are optimal Euler elastics. Simulation results are presented.