Control of the motion of a point object in a viscous medium using a limited force

A solution to a three-dimensional case of a time-optimal control problem for a point object moving in a viscous medium under the action of a control force limited in magnitude in the presence of uniform gravity is constructed in analytical form. For the general case, expressions are found in elementary functions that include two unknown constant vectors that must be found from the boundary conditions. In the case where the final position of the object is not specified, all unknown vectors are found in analytical form. An example of using the obtained relations is given, for which all necessary physical quantities are replaced by one dimensionless parameter.