🧄Kinematics and Vector Calculus of a Rotating Rigid Body

Rigid body motion is characterized by a total acceleration composed of tangential and centripetal components. A key property of rigid bodies is that the divergence of their velocity field is always zero, indicating incompressible motion where the body doesn't expand or contract. The curl of the velocity field is twice the angular velocity, illustrating the relationship between overall angular motion and the local swirling of particles within the body. Additionally, the divergence of the acceleration field is also always zero, directly stemming from its cross-product derivation.

🎬visualize and analyze the motion of a three-dimensional rigid body

The divergence of a rigid body's velocity field is always zero. This demonstrates that the body's motion is incompressible, meaning it's not expanding or contracting. The curl of the velocity field is always equal to twice the angular velocity vector. This shows that the local rotation at any point in the body is directly proportional to the overall rotation rate.

🖊️Mathematical Proof

Kinematics and Vector Calculus of a Rotating Rigid Body | Proof and Derivationviadean on Notion