The differential equation for the vibration of the riser system is derived by means of functional calculus of variation.

Calculation of resonant frequencies of sloshing in a container have been achieved by FEM with calculus of variation, which is able to solve sloshing in variety complex containers.

The calculating formulas of top and bottom pool-surface deformation in TIG full-penetration weld pool is developed based on principles of fluid mechanics and variation calculus.