The long history of research on primary motor cortex has led to a consensus that low-dimensional dynamics can characterize motor population activity, with categorically different activity regimens during distinct phases of movement. Here I build from previous work in the Hatsopoulos Lab to strengthen the claim that primary motor cortex uses distinct patterns of population neural activity which switch during movement execution. I replicate previous findings using parametric Hidden Markov Models and evolve our understanding of these population states by implementing recurrent switching linear dynamical systems models on data from nonhuman primates executing two-dimensional planar reaching movements. Neural population states mapped onto accelerative and decelerative directional components of motion, and linear dynamics of discrete states exhibit relationships with the kinematics they produce. These results further support the view that movement representations in M1 populations decompose movements into accelerative directional elements instead of bell-shaped sub movements. Here I also present a number of potential applications and evolutions of these findings in future experiments and contexts.