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Classical mechanics. Field theory --- Exterior forms. --- Mechanics, Analytic. --- Nonholonomic dynamical systems. --- Vibrations --- Nonholonomic dynamical systems

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51 --- Mathematics --- Differentiable dynamical systems. --- Nonholonomic dynamical systems. --- 51 Mathematics --- Differentiable dynamical systems --- Nonholonomic dynamical systems --- Dynamical systems, Nonholonomic --- Non-holonomic systems --- Nonholonomic systems --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics

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Mathematical physics --- Classical mechanics. Field theory --- Dynamics --- Nonholonomic dynamical systems --- 51-74 --- 51 --- 681.3*J2 --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Dynamical systems, Nonholonomic --- Non-holonomic systems --- Nonholonomic systems --- Differentiable dynamical systems --- Mathematics--?-74 --- Physical sciences and engineering (Computer applications) --- Nonholonomic dynamical systems. --- 681.3*J2 Physical sciences and engineering (Computer applications) --- 51 Mathematics --- 51-74 Mathematics--?-74 --- Solides. --- Solids. --- Systèmes non-holonomes. --- Mécanique --- Mécanique --- Systèmes non-holonomes.

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This book contains a unique description of the nonholonomic motion of systems of rigid bodies by differential algebraic systems. Nonholonomic Motion of Rigid Mechanical Systems from a DAE Viewpoint focuses on rigid body systems subjected to kinematic constraints (constraints that depend on the velocities of the bodies, e.g., as they arise for nonholonomic motions) and discusses in detail how the equations of motion are developed. The authors show that such motions can be modeled in terms of differential algebraic equations (DAEs), provided only that the correct variables are introduced. Several issues are investigated in depth to provide a sound and complete justification of the DAE model. These issues include the development of a generalized Gauss principle of least constraint, a study of the effect of the failure of an important full-rank condition, and a precise characterization of the state spaces.

531.3 --- Differential-algebraic equations --- -Dynamics, Rigid --- Nonholonomic dynamical systems --- Dynamical systems, Nonholonomic --- Non-holonomic systems --- Nonholonomic systems --- Differentiable dynamical systems --- Rigid dynamics --- Algebraic-differential equations --- Differential-algebraic systems --- Equations, Algebraic-differential --- Equations, Differential-algebraic --- Systems, Differential-algebraic --- Differential equations --- Dynamics. Kinetics --- Numerical solutions --- Dynamics, Rigid. --- Nonholonomic dynamical systems. --- Numerical solutions. --- 531.3 Dynamics. Kinetics --- Dynamics, Rigid --- Numerical analysis --- Differentiable dynamical systems. --- Systèmes dynamiques --- Dynamics, rigid --- Dynamique des corps rigides

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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.

Mathematics -- Differential Equations -- General. --- Mathematics. --- Nonholonomic dynamical systems. --- Nonholonomic dynamical systems --- Civil Engineering --- Geometry --- Civil & Environmental Engineering --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Differentiable dynamical systems. --- Dynamical systems, Nonholonomic --- Non-holonomic systems --- Nonholonomic systems --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Engineering. --- Mechanics. --- Computational intelligence. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Computational Intelligence. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Construction --- Industrial arts --- Technology --- Differentiable dynamical systems --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Mechanics, applied. --- Classical Mechanics.