A standard definition of static equilibrium is: A system of particles is in static equilibrium when all the particles of the system are at rest and the total force on each particle is permanently zero. This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next. A pendulum in a stable equilibrium (left) and unstable equilibrium (right) A standard definition of mechanical equilibrium for a particle is: The necessary and sufficient conditions for a particle to be in mechanical equilibrium is that the net force acting upon the particle is zero. The necessary conditions for mechanical equilibrium for a system of particles are: (i)The vector sum of all external forces is zero; (ii) The sum of the moments of all external forces about any line is zero. As applied to a rigid body, the necessary and sufficient conditions become: A rigid body is in mechanical equilibrium when the sum of all forces on all particles of the system is zero, and also the sum of all torques on all particles of the system is zero. A rigid body in mechanical equilibrium is undergoing neither linear nor rotational acceleration; however it could be translating or rotating at a constant velocity. However, this definition is of little use in continuum mechanics, for which the idea of a particle is foreign. In addition, this definition gives no information as to one of the most important and inter sting aspects of equilibrium states – their stability. An alternative definition of equilibrium that applies to conservative systems and often proves more useful is: A system is in mechanical equilibrium if its position in configuration space is a point at which the gradient with respect to the generalized coordinates of the potential energy is zero. Because of the fundamental relationship between force and energy, this definition is equivalent to the first definition. However, the definition involving energy can be readily extended to yield information about the stability of the equilibrium state. In more than one dimension, it is possible to get different results in different directions, for example stability with respect to displacements in the x-direction but instability in the y-direction, a case known as a saddle point. Without further qualification, an equilibrium is stable only if it is stable in all directions. The special case of mechanical equilibrium of a stationary object is static equilibrium. A paperweight on a desk would be in static equilibrium. The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest. In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point, this is called Gomboc. A child sliding down a slide at constant speed would be in mechanical equilibrium, but not in static equilibrium.