16.8 :  剛体の運動方程式

The motion of a rigid body can be described using equations for translational motion and rotational motion about the center of mass.

Newton's Second Law gives the equation of motion for translational motion for a center of mass, G, of the body.

The summation of all the moments created about point G is equal to the rate of change of angular momentum of the body.

If an external force is applied at point A, other than point G, it creates a moment that causes the body to rotate.

The angular momentum of point A can be expressed as a vector product of its relative position and relative velocity with respect to point G.  The time derivatives of angular momentum give the moment of point A.

Summing over all points within the rigid body, the total moment of the system about point G is calculated.

Using the relative acceleration definition and the distributive law for vectors gives the equation for the total moment about point G due to an external force.