In the presented paper, a problem of nonholonomic constrained mechanical systems is treated. New methods in nonholonomic mechanics are applied to a problem of a Forklift-truck robot motion. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. On the other hand, the equations of motion of a Forklift-truck robot are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented.

This paper proposes a mathematical model that allows expanding the scope of research into the mechanism of heat transfer during explosive boiling, cavitation and boiling of multicomponent liquids, identifying the most influential factors and optimizing technological processes. The proposed model takes into account the processes of heat accumulation in the high-boiling part of liquid mixtures (for example, emulsions) and the use of this energy in the process of boiling their thermolabile part, as well as for superheating the resulting steam in steam bubbles. This effect can also be used to evaluate the effects of liquid boiling in thermodynamically unstable regions of liquid media.