Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_33

7/33 The flight simulator is mounted on six hydraulic actuators connected in pairs to their attachment points on the underside of the simulator. By programming the actions of the actuators, a variety of flight conditions can be simulated with translational and rotational displacements through a limited range of motion. Axes \(x\)-\(y\)-\(z\) are attached to the simulator with origin \(B\) at the center of the volume. For the instant represented, \(B\) has a velocity and an acceleration in the horizontal \(y\)-direction of 3.2 ft/sec and 4 ft/sec\(^2\), respectively. Simultaneously, the angular velocities and their time rates of change are \(\omega_x = 1.4 \text{ rad/sec}\), \(\dot{\omega}_x = 2 \text{ rad/sec}^2\), \(\omega_y = 1.2 \text{ rad/sec}\), \(\dot{\omega}_y = 3 \text{ rad/sec}^2\), \(\omega_z = \dot{\omega}_z = 0\). For this instant determine the magnitudes of the velocity and acceleration of point \(A\).