Massijaotuse

Massijaotuse, or mass distribution, refers to how mass is arranged within an object or system. It influences mechanical behavior, stability, and dynamic response, from everyday objects to complex machines.

It is described by a mass density distribution ρ(r) in space or, in a planar body, a surface density σ. In discrete systems, mass is represented by individual masses m_i located at positions r_i. The overall distribution determines the location of the center of mass and how the mass resists rotational acceleration.

The center of mass is the weighted average of all positions: R_cm = (1/M) ∑ m_i r_i or R_cm = (1/M) ∫ r ρ(r) dV. The moment of inertia about a chosen axis is I = ∫ r^2 dm or I = ∑ m_i |r_i×u|^2 for an axis along unit vector u, which governs rotational resistance.

Applications include vehicle design, aerospace, robotics, architecture, and biomechanics. Mass distribution affects stability, handling, vibration modes, and fatigue life, as well as the energy required to accelerate or decelerate an object.

Engineers modify mass distribution by repositioning components, adding ballast, using materials with different densities, or employing hollow structures. Optimization can reduce unwanted vibrations, shift natural frequencies, or improve balance.

Related concepts include center of gravity, balance, and density functions. Analysis methods range from analytical calculations for simple shapes to finite element modeling and experimental measurements.