An Etymological Dictionary of Astronomy and Astrophysics

A set of second order → differential equations for a system of particles which relate the kinetic energy of the system to the → generalized coordinates, the generalized forces, and the time. If the motion of a → holonomic system is described by the generalized coordinates q₁, q₂, …, q_n and the → generalized velocities 

q^.₁, q^.₂, …, q^._n, the equations of the motion are of the form:

d/dt (∂T/∂q^._i) - ∂T/∂q^._i = Q_i (i = 1, 2, …, n), where T is the kinetic energy of the system and Q_i the generalized force.

See also: → Lagrangian; → equation.