A mechanical equilibrium is a state in which a momentum coordinate of a particle, rigid body, or dynamical system is conserved. Usually this refers to linear momentum. For instance, a linear mechanical equilibrium would be a state in which the linear momentum of the system is conserved as the net force on the object is zero. In the specific case that the linear momentum is zero and conserved, the system can be said to be in a static equilibrium although for any system in which the linear momentum is conserved, it is possible to shift to a non-inertial reference frame that is stationary with respect to the object.
In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in configuration space where the gradient with respect to the generalized coordinates of the potential energy is zero.