3.10. The basic equation of the dynamics of the translational motion of a rigid body

Using equations:

and ,

we can write

or

(3.12)

Thus, the center of inertia of a mechanical system moves as a material point, the mass of which is equal to the mass of the entire system and on which a force acts, equal to the main vector of external forces applied to the system. In the general case, the motion of a rigid body can be considered as the sum of two motions: translational with velocity equal to speed center of inertia of the body, and rotation around the center of inertia. Therefore, the last equation is often called the basic equation of the dynamics of the translational motion of a solid.