masspunkt

Masspunkt, or point mass, is a simplifying idealization used in classical mechanics in which all of an object's mass is assumed to be concentrated at a single point, with its physical size neglected relative to the length scales of interest. The position is given by a vector r(t); velocity v = dr/dt; and acceleration a = d^2r/dt^2. The motion is described by Newton's second law, F = m a, with m the mass of the point. For a system of forces, the net force determines the point's acceleration.

This model is especially useful when the spatial extent and internal structure of the body have a negligible effect on the dynamics, such as planetary bodies moving under gravity or everyday objects moving under simple forces. In orbital mechanics, treating bodies as masspoints allows analysis of trajectories under central forces, often in a plane with conserved angular momentum.

Limitations: the masspunkt cannot represent rotation, torque, or effects arising from extended mass distribution, such as moments of inertia or deformation. For problems where shape or rotation affects the motion, a rigid-body or continuum model is required. The masspunkt concept is frequently used within Lagrangian or Hamiltonian formalisms, where the position of the masspoint is a generalized coordinate and forces derive from a potential energy function.

See also center of mass and rigid body motion.