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.

In the article the results of simulation and experimental studies of the movement of a four-wheeled mobile platform, taking into account wheel slip have been presented. The simulation results have been based on the dynamics of the four-wheel mobile platform. The dynamic model of the system motion takes into account the relationship between the active and passive forces accompanying the platform motion, especially during wheel slip. The formulated initial problem describing the motion of the system has been solved by the Runge-Kutta method of the fourth order. The proposed computational model including the platform dynamics model has been verified in experimental studies using the LEO Rover robot. The motion parameters obtained on the basis of the adopted computational model in the form of trajectories, velocities and accelerations have been compared with the results of experimental tests, and the results of this comparison have been included in the paper. The proposed computational model can be useful in various situations, e.g., real-time control, where models with a high degree of complexity are useless due to the computation time. The simulation results obtained on the basis of the proposed model are sufficiently compatible with the results of experimental tests of motion parameters obtained for the selected type of mobile robot.

The main objective of this article is to obtain equations of motion of the spin–stabilized projectile in the presence of non–constant wind. Introducing models allowing utilization of inhomogeneous wind is dictated by new possibilities created by the use of e.g. lidars in the Fire Control Systems (FCS). Constant feed of wind data can replace meteorological messages, increasing the FCS effectiveness. Article contains results of projectile flight simulations which indicate the positive effect that the derived explicit form of the model has when considering software development for modern Fire Control Systems.

In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces. As the configurational spaces within this family are far from being trivial manifolds, the problem of finding the geodesic and geodetic motions presents a real challenge. We have succeeded in finding the solutions to those motions in an explicit parametric form. It is shown that in both cases the solutions can be expressed through the elliptic integrals and elliptic functions, but in the geodetic case some appropriately chosen compatibility conditions for glueing together different branches of the solution are needed. Additionally, an action-angle analysis of the corresponding Hamilton-Jacobi equations is performed for external potentials that are well-suited to the geometry of the problem under consideration. As a result, five different sets of conditions between the three action variables and the total energy of the infinitesimal gyroscopes are obtained.