  This paper presents a novel approach for reconstructing dynamic radiance
fields from monocular videos. We integrate kinematics with dynamic radiance
fields, bridging the gap between the sparse nature of monocular videos and the
real-world physics. Our method introduces the kinematic field, capturing motion
through kinematic quantities: velocity, acceleration, and jerk. The kinematic
field is jointly learned with the dynamic radiance field by minimizing the
photometric loss without motion ground truth. We further augment our method
with physics-driven regularizers grounded in kinematics. We propose
physics-driven regularizers that ensure the physical validity of predicted
kinematic quantities, including advective acceleration and jerk. Additionally,
we control the motion trajectory based on rigidity equations formed with the
predicted kinematic quantities. In experiments, our method outperforms the
state-of-the-arts by capturing physical motion patterns within challenging
real-world monocular videos.
