Massacentrum

Massacentrum, in English often called the center of mass, is the point in a body or system of bodies where the total mass can be considered to be concentrated for purposes of describing translational motion. It depends on how mass is distributed and does not require all parts to be at that location; it characterizes the collective motion of the system.

For a discrete system with N particles of masses m_i at position vectors r_i, the center of mass is R_cm = (1/M) ∑_{i=1}^N m_i r_i, where M = ∑ m_i is the total mass. In a continuous mass distribution with density ρ(r), the center of mass is R_cm = (1/M) ∫ r ρ(r) dV, with M = ∫ ρ(r) dV over the volume V.

The center of mass moves according to the external forces acting on the system. In Newtonian mechanics, M a_cm = F_ext,total, where a_cm is the acceleration of the center of mass. If external forces sum to zero, the center of mass moves with constant velocity; if gravity or other forces are present, they influence the motion through F_ext.

In astronomy, the concept is used as the barycenter or mass center of a gravitational system, such as the solar system or binary stars. Each body orbits around the common center of mass, and in many analyses the motion is simplified by considering the barycenter as the reference point for relative motions.

Calculations of the massacentrum are essential in engineering, physics simulations, robotics, and computer graphics, where it determines rotational behavior, stability, and response to external forces.