Fundamentals of Rigid Body Dynamics in Engineering Mechanics

Rigid body dynamics focuses on the motion analysis of bodies assumed to be perfectly rigid, meaning the distance between any two points on the body remains constant during motion, and deformation is neglected. The overall motion is described by the translation of the center of mass and rotation about an axis or point. Newton's second law governs the translational motion with the relation $\mathbf{F}_{\text{net}} = m \mathbf{a}_{\text{cm}}$, where $m$ is the mass and is the acceleration of the center of mass. Rotational motion is described by Euler's equations: , where is the net torque, the moment of inertia tensor, and the angular acceleration. Angular velocity () and angular acceleration quantify rotational kinematics. The total kinetic energy of a rigid body combines translational and rotational parts: . Understanding rigid body dynamics is crucial in mechanical system design such as gears, engines, and robotics, providing insight into structural stability under dynamic loads, and supporting advanced studies in vibration and multibody dynamics.