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Control theory. --- Differential algebraic equations. --- Nonlinear theories.

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Differential-algebraic equations. --- Dynamics, Rigid. --- Mechanics, Analytic. --- Mechatronics.

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This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation,  the KP equation,  the nonlinear Schrodinger equation,  the Davey and Stewartson equations, the Boussinesq equations in geophysics,  the Navier-Stokes equations and the boundary layer problems.  In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions,  symmetry transformations,  linearization techniques  and  special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.

Mathematics --- Partial differential equations --- Differential equations --- Mathematical physics --- differentiaalvergelijkingen --- toegepaste wiskunde --- wiskunde --- fysica --- Differential equations. --- Differential-algebraic equations.

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The present work deals with the inverse dynamics simulation of underactuated multibody systems. In particular, the study focuses on solving trajectory tracking control problems of differentially flat underactuated systems. The use of servo constraints provides an approach to formulate trajectory tracking control problems of underacutated systems, which are also called underactuated servo constraint problems.

index reduction --- servo constraints --- differential-algebraic equations --- Inverse Dynamik --- unteraktuierte Systeme --- differential-algebraische GleichungenInverse dynamics --- Servobindungen --- Indexreduktion --- underactuated mechanical systems

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The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed. The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems. The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. Th

Geometry, Plane. --- Differential-algebraic equations. --- Algebraic-differential equations --- Differential-algebraic systems --- Equations, Algebraic-differential --- Equations, Differential-algebraic --- Systems, Differential-algebraic --- Differential equations --- Plane geometry