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The present review is concerned with the motion of aerosol particles, including that under the exposure to external fields, with special focus being put on the problems related to the similarity theory and invariants that manifest themselves as symmetry in physics. Research on the mechanics of aerosols is extremely important for managing environmental practices. Ultrasonic and electrostatic effects are used in technological processes for cleaning industrial aerosol emissions. In addition, aerosol systems are commonly used to prevent emergency situations (fire extinguishing, fog deposition). Understanding these processes requires knowledge of aerosol mechanics. At the same time, fundamental laws of particulate matter behavior have not been established until now, especially in the presence of external fields. In this paper, we consider the main similarity criteria that are applied for aerosol description. The motion of aerosol particles in the gravitational, electric, and ultrasonic fields is described. The results from studies into acoustic and electrostatic aerosol coagulations are presented herein. [ABSTRACT FROM AUTHOR]