Magnetic materials are critically important in a wide range of application areas including data storage, medicine, energy harvesting, and refrigeration. Atomistic numerical simulations of magnetic materials can provide important insight in these applications because they offer the ability to track phenomena such as magnon-phonon interactions, ultrafast demagnetization processes, and magnetization and energy at time and length scales that can be difficult to observe experimentally. Spin-lattice dynamics, a classical atomistic simulation method that models atomic magnetic moments and atomic displacements simultaneously, is able to capture these phenomena. Unfortunately, energy stability can be a challenge in spin-lattice dynamics simulations and angular momentum artifacts are a known issue in atomistic models of periodic systems. Both of these problems can cause errors in the evolution of spin orientations and atomic positions, leading to unphysical predictions of temperature, magnetization, and thermal-magnetic coupling in magnetic materials. This dissertation presents an improved computational model for spin-lattice dynamics simulations developed to address the above challenges. The model offers superior energy and magnetization conservation and the ability to quantify lattice angular momentum changes generated by spin relaxation processes in bulk materials. The improvements made in this work advance spin-lattice dynamics as a computational tool for the design and analysis of magnetic materials.