Some large-scale natural phenomena and unexpected experiments are analyzed. It is proved that they can be explained by gravitomagnetism existence and significant gravitomagnetic forces. On the same basis it is proved that a generator using the gravitational conservative forces source energy for work performance can exist and this does not contradict the energy conservation law. A new solution of Maxwell's equations for gravitomagnetism, used in order to create the various models of phenomena (sand-devil, sea current, rotary stream, funnel, water soliton, water and sand tsunami, turbulent flows, additional (non-Newtonian) forces of celestial bodies’ interaction) is proposed. A detailed proof for interested reader is given. Experimental validations of the theory are considered. Explanations of experiments that have not been justified until now are proposed.