When vehicles are launched (e.g. from a ramp) or drive off a cliff, large angular motions about several axes may ensue before the first impact. This paper presents a rational approach to solving for the large angular motions in terms of Euler angles, making use of Euler's equations for rotation of rigid bodies. Wheel forces are assumed to act vertically to the horizontal surface on which motion commences. The method is amenable to braking forces and side loads (not presented). The appendix provides a brief resume of the linearized equations of motion including braking.