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Many studies decompose human motion into local motion in a frame attached to the root joint and global motion of the root joint in the world frame, treating them separately. However, these two components are not independent. Global movement arises from interactions with the environment, which are, in turn, driven by changes in the body configuration. Motion models often fail to precisely capture this physical coupling between local and global dynamics, while deriving global trajectories from joint torques and external forces is computationally expensive and complex. To address these challenges, we propose using whole-body linear and angular momentum as a constraint to link local motion with global movement. Since momentum reflects the aggregate effect of joint-level dynamics on the body's movement through space, it provides a physically grounded way to relate local joint behavior to global displacement. Building on this insight, we introduce a new loss term that enforces consistency between the generated momentum profiles and those observed in ground-truth data. We evaluate our loss on the global motion recovery task. Incorporating our loss reduces foot sliding and jitter, improves balance, and preserves the accuracy of the recovered motion.
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