We develop a general numerical approach to inverse problems of vehicle dynamics, suitable for both e xed- and rotating-wing aircrafts. The formulation is based on an energy-preserving e nite element in time for rigid body dynamics that ensures unconditional stability according to the energy method. The nonlinear inverse problem of motion is solved by assembling a suitable number of time elements over the time interval of interest and enforcing the appropriate boundary conditions. The capabilities and performance of the proposed procedure are illustrated by means of numerical examples. Nomenclature Di = ti, ti C 1; time element d ± (¢)/dt = corotational derivative I3, I6 = 3 £ 3 and 6 £ 6 identity matrices J = spatial inertia dyadic m = mass (O, ii) = e xed frame of origin O, i D 1, 2, 3 (P, ei) = embedded frame of origin P, i D 1, 2, 3 p = l, h; generalized momentum vector (linear, angular ) R(A) = rotation tensor associated with the rotation vector A r = f, m; generalized force vector (force, torque ) T = period of the maneuver t = time w = v, !; generalized velocity vector (linear, angular ) x = P i O; position vector of P in (O, ii) ® = direction cosine matrix D t = ti C1 i ti; time step ± = d a, d e, d r, d T; aileron, elevator, rudder, and thrust