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Our work is a step in the direction set by Newton and Euler to propose a general mathematical model for mechanical systems whose particles can experience displacements and turns with velocities v and . They are named as those of Cosserat-Zhilin and generate a new version of Newtonian mechanics based on notions of vector calculus - sliders and screw measures (bi-measures). In the case where Stocks theorem is applicable, differential equations of motion or tensionare defined for main classes of Cosserat-Zhilin systems.The work defines multiplicative groups which represent the measure ofstress...

Applications of mechanics are inseparably linked with many different theories such as, e.g., that of stability and system one. This book is unique in its emphasis on developing the following topics: 1. axiomatics of Newtonian mechanics where all known mechanical systems are treated from the general viewpoint (namely, a material particle, a rigid body and a continuum); 2. construction of control forces ensuring preplanned behavior of finite-dimensional mechanical systems and their robustness; 3. satellite attitude control; 4. precession theory of time-varying gyro systems; 5. abstract...

There is given the complete exposition of a mathematical formalism and the working tools of mechanics of multibody systems based on methodology of the system analysis. Essentially in a new fashion the problem of designing of the differential equations of constraints of a general kind of multibody systems with environment bodies is represented. Two algorithms of direct analytical designing of a reverse matrix of kinetic energy of system are developed, passing stages of designing of the matrix and its subsequent reversing. The created algorithms are most numerically economic among known....

Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and...

The idea of optimization runs through most parts of control theory. The simplest optimal controls are preplanned (programmed) ones. The problem of constructing optimal preplanned controls has been extensively worked out in literature (see, e. g., the Pontrjagin maximum principle giving necessary conditions of preplanned control optimality). However, the concept of op timality itself has a restrictive character: it is limited by what one means under optimality in each separate case. The internal contradictoriness of the preplanned control optimality ("the better is the enemy of the good")...