massadistributie

Massadistributie, or mass distribution, describes how mass is spread within a body or system. For a continuous distribution, mass density is described by a density function rho(r), so the total mass M is the volume integral M = ∫ rho dV over the region of interest. The center of mass is the mass-weighted average position r_cm = (1/M) ∫ r rho dV, and the inertia properties are captured by the inertia tensor I = ∫ [|r|^2 δ_ij − r_i r_j] rho dV. For discrete masses, mass distribution is represented by a set of point masses m_i at positions r_i, with M = Σ m_i and r_cm = (1/M) Σ m_i r_i.

Distributions can be uniform, with constant density, in which case symmetry places the center of mass at the geometric center; or non-uniform, where density varies across the object or region, shifting the center of mass and affecting gravitational and inertial behavior. Non-uniform distributions also lead to nontrivial rotational properties and higher-order mass moments.

Applications span engineering, physics, and earth and space sciences. In engineering, mass distribution influences balance, vibration modes, and stiffness; in physics, it determines gravitational fields and orbital dynamics; in astronomy and cosmology, the visible matter’s distribution and dark matter halos govern galaxy rotation curves and lensing. Measurement and modeling approaches include direct weighing, imaging and tomography for density profiles, and dynamical methods such as analyzing motion under gravity or simulating N-body systems.

Understanding mass distribution provides a foundational link between an object's internal structure and its external behavior.