Inertial Equilibration: Inertial Invariance

This lecture covers the concept of inertial invariance in mechanically balanced systems, where the inertia tensor remains constant throughout the workspace. It also discusses inertial equilibration, where the system's momentum, angular velocity, and inertia tensor remain constant. Different types of equilibration, such as partial and local equilibration, are explained, along with the classification of equilibrations based on force and moment balancing. The lecture delves into the implementation of passive equilibration through mass distribution and kinematic coupling. Active force and moment equilibration are explored, involving trajectory planning and additional actuators. The concept of active dynamic balancing is introduced, highlighting its sensitivity to external linear and angular accelerations. References to related research and publications in the field of mechanical equilibration are provided.