A general approach to the derivation of equations of motion of as holonomic, as nonholonomic systems with the constraints of any order is suggested. The system of equations of motion in the generalized coordinates is regarded as a one vector relation, represented in a space tangential to a manifold of all possible positions of system at given instant. The tangential space is partitioned by the equations of constraints into two orthogonal subspaces. In one of them for the constraints up to the second order, the motion low is given by the equations of constraints and in the other one for ideal constraints, it is described by the vector equation without reactions of connections. In the whole space the motion low involves Lagrangian multipliers. It is shown that for the holonomic and nonholonomic constraints up to the second order, these multipliers can be found as the function of time, positions of system, and its velocities. The application of Lagrangian multipliers for holonomic systems permits us to construct a new method for determining the eigenfrequencies and eigenforms of oscillations of elastic systems and also to suggest a special form of equations for describing the system of motion of rigid bodies. The nonholonomic constraints, the order of which is greater than two, are regarded as programming constraints such that their validity is provided due to the existence of generalized control forces, which are determined as the functions of time. The closed system of differential equations, which makes it possible to find as these control forces, as the generalized Lagrange coordinates, is compound. The theory suggested is illustrated by the examples of a spacecraft motion. The book is primarily addressed to specialists in analytic mechanics.
Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.
This book is a unique collection of experimental data in the field of internal friction, anelastic relaxation, and damping properties of metallic materials. It reviews virtually all anelastic relaxation phenomena ever published. The reader is also supplied with explanations of the basic physical mechanisms of internal friction, a summary of typical effects for different groups of metals, and more than 2000 references to original papers.
This book challenges the common perception of authoritarian regimes as incompatible with federalism and decentralization. It examines how the leaders of Russia, Ukraine, and Kazakhstan have managed to exploit federalism and decentralization as useful instruments to help them preserve control, avoid political instability, and to shift blame to the regional authorities in times of crises and policy failures. The authors explain how post-Soviet authoritarian regimes balance the advantages and risks and emphasize the contradictory role of external influences and threats to the institutional design of federalism and decentralization. Advancing our understanding of how the institutions of federalism and decentralization are skillfully constrained, but at the same time used by authoritarian incumbents, they show that federalism and decentralization matter in non-democracies, though the nondemocratic character of the political systems greatly modifies their effects. The authors show the implication of the COVID-19 crisis and current Russian war against Ukraine for the center-regional relations in Russia, Ukraine, and Kazakhstan. This book will be of interest to scholars and students of post-Soviet politics, decentralization, federalism, and modern authoritarianism.
As the basis for this book, the authors have analyzed more than 100,000 ultrasound examinations performed between 1995 and 2008 in patients with thyroid and parathyroid disease, as well as many thousands of diagnostic and therapeutic ultrasound-guided minimally invasive procedures. The opening chapters include discussion of current ultrasound techniques, pitfalls, and ultrasound examination of the thyroid in children. Detailed attention is then devoted to findings in the normal thyroid and in the presence of diffuse and focal changes. Further chapters focus on such topics as the role of ultrasound after thyroid surgery and ultrasound diagnosis of parathyroid disease, recurrent goiter, and neck masses. Ultrasound-guided minimally invasive techniques, such as fine-needle aspiration biopsy and percutaneous laser ablation, are considered in depth. This up-to-date and richly illustrated book will interest and assist specialists in ultrasound diagnostics, radiologists, endocrinologists, and neck surgeons.
A general approach to the derivation of equations of motion of as holonomic, as nonholonomic systems with the constraints of any order is suggested. The system of equations of motion in the generalized coordinates is regarded as a one vector relation, represented in a space tangential to a manifold of all possible positions of system at given instant. The tangential space is partitioned by the equations of constraints into two orthogonal subspaces. In one of them for the constraints up to the second order, the motion low is given by the equations of constraints and in the other one for ideal constraints, it is described by the vector equation without reactions of connections. In the whole space the motion low involves Lagrangian multipliers. It is shown that for the holonomic and nonholonomic constraints up to the second order, these multipliers can be found as the function of time, positions of system, and its velocities. The application of Lagrangian multipliers for holonomic systems permits us to construct a new method for determining the eigenfrequencies and eigenforms of oscillations of elastic systems and also to suggest a special form of equations for describing the system of motion of rigid bodies. The nonholonomic constraints, the order of which is greater than two, are regarded as programming constraints such that their validity is provided due to the existence of generalized control forces, which are determined as the functions of time. The closed system of differential equations, which makes it possible to find as these control forces, as the generalized Lagrange coordinates, is compound. The theory suggested is illustrated by the examples of a spacecraft motion. The book is primarily addressed to specialists in analytic mechanics.
Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.
Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). This first volume of the textbook contains the parts “Kinematics” and “Dynamics”. The part “Kinematics” presents in detail the theory of curvilinear coordinates which is actively used in the part “Dynamics”, in particular, in the theory of constrained motion and variational principles in mechanics. For describing the motion of a system of particles, the notion of a Hertz representative point is used, and the notion of a tangent space is applied to investigate the motion of arbitrary mechanical systems. In the final chapters Hamilton-Jacobi theory is applied for the integration of equations of motion, and the elements of special relativity theory are presented. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.
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