THE TASK OF PURSUING AN OBJECT FROM THE SURFACE LOCATED ABOVE THE SURFACE OF THE PURSUED

Abstract

The purpose of this article is to describe a mathematical model of the pursuit problem in the
case when the pursued and pursuing objects move along different surfaces placed one above the
other. Orthonormal dynamic bases, which are determined by the vectors of velocities and normals to
the surfaces, are introduced on the surfaces under consideration at the points where objects are located,
and the construction of tangent planes is performed. Coordinates of our model's opponent are
projected onto each specified plane for analysis and decision making. Velocities of objects in the
model are constant in their magnitude. Inertness of objects is modeled using the angular velocity of
rotation, which is essential in the described model. As a result of the research, an iterative algorithm
leading to achievement of the threshold value in the horizontal plane of projections has been obtained.
According to the research results, a dynamic visualization of the pursuit task has been made,
which provides visibility to the results obtained.