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51 --- Mathematics --- Bifurcation theory. --- Boundary value problems. --- Elasticity. --- Von Kármán equations. --- 51 Mathematics --- Elasticity --- Nonlinear mechanics --- Élasticité non linéaire --- Équations aux dérivées partielles non linéaires. --- Problèmes aux limites. --- Boundary value problems --- Differential equations, Nonlinear

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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