This paper presents a new Model Predictive Control (MPC) framework for controlling various dynamic movements of a quadrupedal robot. System dynamics are represented by linearizing single rigid body dynamics in three-dimensional (3D) space. Our formulation linearizes rotation matrices without resorting to parameterizations like Euler angles and quaternions, avoiding issues of singularity and unwinding phenomenon, respectively. With a carefully chosen configuration error function, the MPC control law is transcribed into a Quadratic Program (QP) which can be solved efficiently in realtime. Our formulation can stabilize a wide range of periodic quadrupedal gaits and acrobatic maneuvers. We show various simulation as well as experimental results to validate our control strategy. Experiments prove the application of this framework with a custom QP solver could reach execution rates of 160 Hz on embedded platforms.