The developed technique of mathematical description of structurally complex forest soil and vegetation community is presented on the basis of the finite element method within the framework of modeling the work of forest tillage aggregates. The soil is thus represented in the form of spherical-shaped elements interacting in a certain way with each other, as well as with the working surfaces of forest machines. It was noted that the interaction of soil particles is of viscoelastic nature. An algorithm for calculating the forces of elements interaction is presented, depending on their spacing. Composed equations of motion describing the change in the dynamic state of the soil over time are presented. Movement of spherical elements within the framework of the mathematical model is considered in a rectangular parallelepiped with specified dimensions. The authors noted the possibility of modeling the interaction of the forest machines attachments with the soil environment, including, in particular, the roots of plants, which are presented by a set of spherical elements located in a geometric region that has the form of the cylindrical upper part of the root system, which transforms smoothly into the roots of a conical shape. The initial allocation of the particles that make up the root of the plant is done by spacing a certain number of base points along the axial lines with an equal step.

A mathematical technique is developed to describe the interaction process between a forest disk plow and soil medium when fire mineralized breaks are developed. Disk plowing provides insufficient quality of a furrow slice rotation therefore it is recommended to equip spherical disks with additional breasts of a plow-bottom type. To determine the optimal parameters of the developed design, the interaction of the working organ with the soil medium is simulated using the finite element method, where the soil and the spherical disk are represented as a set of a large number of separate spherical elements interacting in a certain way. The authors describe the technique of composing the equation of plane to simulate the operation of a plow-bottom breast. A special singling algorithm is used for uniform distribution of spherical elements, when the number of initially created points is larger than required, and the points located in dense areas are eventually removed. A computer program was developed to implement the mathematical model in the form of a system of differential equations and to conduct theoretical experiments. In the course of the computer experiment the disc with the fixed parameters moved linearly for a certain distance and the configuration of the developed furrow and the quality of soil cultivation and the energy capacity of the process were evaluated.

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