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In this paper, an approach to numerical integration of equations governing motion of constrained mechanical systems is suggested. In this approach, unknown reaction forces acting on the system are treated as controls, and the algebraic equations that these reactions satisfy, as control goals. Based on the suggested approach, an algorithm for numerical solving rolling equations is developed. The discussion is illustrated by the example of application of the algorithm to solve the problem of a heavy wheel rolling along a curvilinear profile without slippage.

Control of an unmanned aerial vehicle (UAV) requires knowledge of information on its attitude, which is estimated with the help of satellite receivers, gyros, accelerometers, and magnetometers. To ensure correct measurements, all sensors are to be calibrated before the flight. However, the ground-based calibration of the magnetometer cannot ensure correct measurements of Earth's magnetic field because of the additional magnetic fields created by strong currents arising in the electric motor circuits in the course of flight. The paper addresses the problem of fine compass calibration to determine in-flight calibration parameters. Two calibration techniques are proposed and discussed. The discussion is illustrated by results of field experiments with an octocopter Triumph-F1.

A finite-dimensional nondegenerate system of algebro-differential equations with discontinuances is considered. An equivalent system of discontinuous differential equations is constructed. Conditions of right-hand uniqueness of solution and of convergence of numerical methods are given.

Consideration was given to a finite-dimensional system of algebro-differential equations with discontinuities. Solution was determined in a general form, and the existence theorem was proved for the nondegenerate case.

The Lagrange equations of motion are written for a mechanical system consisting of kinematic dry-friction pairs. These equations are not solved for higher derivatives and constraint forces. The definition of a solution to them is given. Theorems on the uniqueness and existence of such a solution are formulated under certain sufficiently general additional assumptions. The results obtained develop and complement the mechanical theory of systems with dry friction [1‐6]. 1. The equations of motion are derived by the method of elimination of constraints, which is described in papers [7, 8]. According to this method, an initial system with constraints is changed for another system in which frictional constraints are replaced by reaction forces N 1 , …, and N m and friction forces. To describe the position of such a system, additional coordinates q n + 1 , …, q n + m are introduced along with the initial coordinates q 1 , …, q n . For the extended system under consideration, which is free of frictional constraints, an expression for kinetic energy T and the Lagrange equations of motion can be immediately determined. The kinetic energy T is assumed to be the quadratic form with respect to