Puntmassas

Puntmassas are idealized particles used in physics to model discrete, localized masses whose physical size is negligible compared to the distances between them. They are commonly employed in classical mechanics and gravitational dynamics to simplify the study of multiple bodies interacting through forces such as gravity or electrostatics. In this framework, each puntmassa is characterized by a mass, a position, and a velocity that evolve over time according to the governing forces.

The mathematical model assigns to each puntmassa i a mass m_i and a position r_i(t). The motion is governed by Newton's second law, typically written as m_i d^2 r_i/dt^2 = ∑_{j≠i} F_{ij}, where F_{ij} is the force exerted on i by j. In gravitational problems, F_{ij} = G m_i m_j (r_j − r_i)/|r_j − r_i|^3, leading to coupled equations of motion. The system's potential energy is U = −G ∑_{i<j} m_i m_j/|r_i − r_j|, and the kinetic energy is T = 1/2 ∑ m_i |v_i|^2. The total mass M = ∑ m_i, the total linear momentum P = ∑ m_i v_i, and the total angular momentum L = ∑ m_i r_i × v_i are conserved in the absence of external forces.

In practice, puntmassas are used in numerical simulations (the N-body problem). To handle near-collisions and singularities, techniques such as softening parameters or regularization and symplectic integrators are employed. Limitations include the neglect of finite size, tidal effects, and internal structure of bodies. They remain useful in celestial mechanics, galactic dynamics, and education as a first-order approximation of multi-body systems.