Consider a point particle that moves along a path which is described by a function r ( t ) from point A , where r ( t = t 0 ) , to point B , where r ( t = t 1 ) . It is possible that the particle moves from A to B along a nearby path described by r ( t ) + δ δ r ( t ) , where δ δ r ( t ) is called the variation of r ( t ) . The variation δ δ r ( t ) satisfies the requirement δ δ r ( t 0 ) = δ δ r ( t 1 ) = 0 . The scalar components of the variation δ δ r 1 ( t ) , δ δ r 2 ( t ) and δ δ r 3 ( t ) are called virtual displacements. This can be generalized to an arbitrary mechanical system defined by the generalized coordinates q i , i = 1 , 2 , . . . , n . In which case, the variation of the trajectory q i ( t ) is defined by the virtual displacements δ δ q i , i = 1 , 2 , . . . , n .