We propose a novel kinematic prior for 3D human pose tracking that allows predicting the position in subsequent frames given the current position. We first define a Riemannian manifold that models the pose and extend it with its Lie algebra to also be able to represent the kinematics. We then learn a joint Gaussian mixture model of both the human pose and the kinematics on this manifold. Finally by conditioning the kinematics on the pose we are able to obtain a distribution of poses for subsequent frames that which can be used as a reliable prior in 3D human pose tracking. Our model scales well to large amounts of data and can be sampled at over 100,000 samples/second. We show it outperforms the widely used Gaussian diffusion model on the challenging Human3.6M dataset.