Modeling complex rigid motion across large spatiotemporal spans remains an unresolved challenge in dynamic reconstruction. Existing paradigms are mainly confined to short-term, small-scale deformation and offer limited consideration for physical consistency. This study proposes PMGS, focusing on reconstructing Projectile Motion via 3D Gaussian Splatting. The workflow comprises two stages: 1) Target Modeling: achieving object-centralized reconstruction through dynamic scene decomposition and an improved point density control; 2) Motion Recovery: restoring full motion sequences by learning per-frame SE(3) poses. We introduce an acceleration consistency constraint to bridge Newtonian mechanics and pose estimation, and design a dynamic simulated annealing strategy that adaptively schedules learning rates based on motion states. Furthermore, we devise a Kalman fusion scheme to optimize error accumulation from multi-source observations to mitigate disturbances. Experiments show PMGS's superior performance in reconstructing high-speed nonlinear rigid motion compared to mainstream dynamic methods.

翻译：在动态重建领域，对复杂刚体运动在大时空跨度下的建模仍是一个尚未解决的挑战。现有范式主要局限于短期、小尺度的形变，且对物理一致性的考量有限。本研究提出PMGS，专注于通过3D高斯溅射技术重建抛射体运动。其工作流程包含两个阶段：1）目标建模：通过动态场景分解与改进的点云密度控制，实现以目标为中心的重建；2）运动恢复：通过学习逐帧SE(3)位姿恢复完整运动序列。我们引入加速度一致性约束以衔接牛顿力学与位姿估计，并设计了一种动态模拟退火策略，该策略能根据运动状态自适应调整学习率。此外，我们提出一种卡尔曼融合方案，通过优化多源观测的误差累积来抑制干扰。实验表明，相较于主流动态重建方法，PMGS在高速非线性刚体运动重建方面展现出更优的性能。