The study from the position of theoretical mechanics discusses some aspects of the jump down of the "gymnast" – athlete (or the robot – "gymnast") from the "crossbar". We discuss all phases of the jump in the planar case. "Gymnast" body is modeled as three-links physical pendulum, however, after departing from the "crossbar" and lowering the "hands" model the dynamic system becomes two-links pendulum. For a two-links model in the regime of "kinematic" control, we deal with the process of lowering hands, free flight, the output of the "legs" on the frame (absolutely inelastic impact) and holding operation in support phase with the aim of vertical stabilize of the pendulum system. Mode "kinematic control" means the ability to instantly change the angle between the links of the body (in some limits). For each of the phases of movement, we found a convenient form of describing dynamical equations. These equations are based on the use as a variable momentum of the system relative to various points of the body or space. The order of this system of equations is lower than for the full order system. The stage of calm "gymnast" that occurs after the foot on the surface of the support, will also be examined on the basis of special system of equations of this type. It was shown, that we can use numerical analysis to build the region of controllability for transition of the two-links model in a state of stabilization, corresponding to the equality of the horizontal coordinate of the support foot and the center of gravity of the two-links pendulum system. The algorithm of stabilizing control is designed. The results of presented of the analysis of the problem allow us to construct a convenient approximate model of the phenomenon as a whole, and to use it to control a robotic counterpart. As an example, it is considered one of the cases of motion that corresponds to the anthropomorphic model.

We consider dynamic model of the motion in the sagittal plane of the exoskeleton of lower limbs, integrated with the similar model of the human operator by means of straps with one or two controllable actuators in each leg. The exoskeleton is additionally loaded with heavy point weight. Considered models of visco-elastic and the rigid attachment of the exoskeleton to the person. The model also takes into account the dynamics of the electric actuators. We study the possibility of designing control systems for various options of the actuators in the joints of the exoskeleton (knee or both in the knee and hip), which also take into account the different degrees of force action of the human operator on the process of movement. The synthesis is based on the method of solving the inverse tasks of the dynamics. The analytical motion control for exoskeleton was designed, which provided locomotion to the hip and knee joints in accordance with the selected desired mode. Synthesis of the control system was carried out on the example of a flat, single support for comfortable walking. The algorithms provide a good quality performance of a given motion and an acceptable cost of energy from the human operator. With sufficient size nominal torque for actuators, the exoskeleton is able to provide substantial assistance to the person carrying the heavy weight, as is evident from the analysis of energy costs. The best energy results with good precision implementation can be obtained in the case of a perfectly rigid model, in which the design of the exoskeleton and the human body are one.

Within the framework of the rigid body hypothesis, the influence of external torques acting on a rotating water lens in a stratified ocean is examined and a hypothesis about the angular motion of objects of such kind is constructed. The structure of the external torques acting on the lens is investigated and their magnitudes and influence on the overall picture of the motion of the lens about its centre of mass are estimated. It is shown that the hydrostatic buoyancy torque is the most important of such torques, it being orders of magnitude greater than the Coriolis torque and the torque due to virtual masses, and also the gravitational torque and other torques. The friction torque can promote stabilization of the angular motion and lead to the appearance of a steady regime. The results obtained are in agreement with the observed motion of oceanic formations.

We study the energy expenditures and the peak values of control torques which a human operator must apply in the process of exoskeleton displacement for various types of regular, plane, and single-support gaits. The obtained results allow us to estimate the performance of the passive exoskeleton apparatus.

The problem of time-optimal swinging of a double pendulum with the upper suspension point (and some other pendulum-type mechanical systems) from the stable lower position into the unstable upper position is solved. The angle between the links or, more precisely, the angular velocity of this angle is controlled. This angular velocity and the angle itself can vary within bounded intervals.

The problem of the equilibrium shapes of rotating vortices in a stratified ocean, which is in a statically stable state, is considered within the framework of the model of an ideal incompressible fluid. An equilibrium shape is a surface on which the pressures in the vortex and in the ocean are equal, in which case, on this surface the normal components of the velocities of the media are equal to zero, but a discontinuity of the tangential components is allowed. The case of stratification of the media along the local vertical is considered. The external medium (the ocean) may consist of several layers, differing sharply in density.

A model formulation of the problem of the equilibrium shapes of a rotating oceanic lens of uniform density, the centre of which is at rest relative to the Earth is considered. All the components of the angular velocity of rotation of the Earth are taken into account, unlike, for example, in oceanography, where only one vertical component of this velocity is considered. The ocean surrounding the lens is assumed to be at rest, and its density is assumed to have a linear distribution. The equilibrium shape is the surface on which the pressures in the lens and in the ocean are equal, and here, on this surface, discontinuity of the tangential components of the velocities is permitted at points of both media. The exact solution of this problem, obtained earlier in [1] for the case of a uniform gravitational field of the Earth, is extended to the case of a potential gravitational field, approximating the actual field, taking into account of the variable nature of the centrifugal force field. The solution is approximate in nature and makes it possible, for example, to indicate the lower limit of the range of angular velocities of proper rotation of the lens, starting from which a more precise allowance for the gravitational field of the Earth is necessary, since it begins to have a considerable effect on the type of equilibrium shape sought. (C) 2004 Elsevier Ltd. All rights reserved.