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Motion prediction is a classic problem in computer vision, which aims at forecasting future motion given the observed pose sequence. Various deep learning models have been proposed, achieving state-of-the-art performance on motion prediction. However, existing methods typically focus on modeling temporal dynamics in the pose space. Unfortunately, the complicated and high dimensionality nature of human motion brings inherent challenges for dynamic context capturing. Therefore, we move away from the conventional pose based representation and present a novel approach employing a phase space trajectory representation of individual joints. Moreover, current methods tend to only consider the dependencies between physically connected joints. In this paper, we introduce a novel convolutional neural model to effectively leverage explicit prior knowledge of motion anatomy, and simultaneously capture both spatial and temporal information of joint trajectory dynamics. We then propose a global optimization module that learns the implicit relationships between individual joint features. Empirically, our method is evaluated on large-scale 3D human motion benchmark datasets (i.e., Human3.6M, CMU MoCap). These results demonstrate that our method sets the new state-of-the-art on the benchmark datasets. Our code will be available at https://github.com/Pose-Group/TEID.