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 The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who like to enter this field.

Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Mathematical Applications in the Physical Sciences. --- Mathematical Methods in Physics. --- Mathematical physics. --- Physique --- Physique mathématique --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Equations of motion. --- Motion equations --- Gravitation. --- Mechanics --- Lagrange equations --- Physical mathematics --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Properties

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The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics.Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives. To this set of problems belongs the description of the collective behaviours of complex systems composed by a large enough n

Monte Carlo method. --- Equations of motion. --- Multiagent systems --- Agent-based model (Computer software) --- MASs (Multiagent systems) --- Multi-agent systems --- Systems, Multiagent --- Intelligent agents (Computer software) --- Motion equations --- Mechanics --- Lagrange equations --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Numerical analysis --- Numerical calculations --- Stochastic processes --- Mathematical models. --- Monte Carlo method --- Equations of motion --- E-books

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New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevatorsControl applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states. In PDE Control of String-Actuated Motion, Ji Wang and Miroslav Krstic develop control algorithms for these complex PDE-ODE systems evolving on time-varying domains.Motivated by physical systems, the book’s algorithms are designed to operate, with rigorous mathematical guarantees, in the presence of real-world challenges, such as unknown parameters, unmeasured distributed states, environmental disturbances, delays, and event-triggered implementations. The book leverages the power of the PDE backstepping approach and expands its scope in many directions.Filled with theoretical innovations and comprehensive in its coverage, PDE Control of String-Actuated Motion provides new design tools and mathematical techniques with far-reaching potential in adaptive control, delay systems, and event-triggered control.

Boundary value problems. --- Cables --- Control theory. --- Differential equations, Partial. --- Equations of motion. --- Loads (Mechanics) --- Loads (Mechanics). --- SCIENCE / Mechanics / Dynamics. --- Vibration. --- Strains and stresses --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Motion equations --- Mechanics --- Lagrange equations --- Partial differential equations --- Dynamics --- Machine theory --- Accelerometer. --- Actuator. --- Adaptive control. --- Aircraft. --- Algorithm. --- Altitude. --- Ammeter. --- Amplitude. --- Angle of attack. --- Attitude control. --- Belt (mechanical). --- Bending. --- Buoyancy. --- Cape Crozier. --- Center of mass (relativistic). --- Center of pressure (fluid mechanics). --- Centrality. --- Centrifugal force. --- Chemical bond. --- Coanda effect. --- Combination. --- Compressibility. --- Contact force. --- Contour line. --- Control limits. --- Control reversal. --- Control variable. --- Convection. --- Coordinate system. --- Coupling. --- Drill bit. --- Dynamic pressure. --- Eigenfunction. --- Elastic instability. --- Elevon. --- Empennage. --- Equation. --- Flapper valve. --- Flight control surfaces. --- Force. --- Frequency domain. --- Frequency response. --- Fuselage. --- Gangway (nautical). --- Hamilton's principle. --- Imagery. --- Increment and decrement operators. --- Inference. --- Initial condition. --- Inspection. --- Laminar flow. --- Limit load (physics). --- Limit set. --- Linearization. --- Longitudinal mode. --- Loop around. --- Mach number. --- Main effect. --- Motion control. --- Motion planning. --- Newton's laws of motion. --- Open loop. --- Order of magnitude. --- Partial differential equation. --- Pitch angle (particle motion). --- Powered lift. --- Pressure. --- Propulsion. --- Publishing. --- Requirement. --- Rotation around a fixed axis. --- Shackle. --- Shear flow. --- Simultaneity. --- Skin friction drag. --- Solver. --- Specific impulse. --- Spiral model. --- Spline interpolation. --- State-space representation. --- Subroutine. --- Thrust vectoring. --- Torsion (mechanics). --- Torsional vibration. --- Trajectory. --- Transfer function. --- Transformation matrix. --- Transonic. --- Unit vector. --- Upper and lower bounds. --- Vector field. --- Vector projection. --- Vertical stabilizer. --- Vestibular system. --- Vibration control. --- Wind tunnel. --- Wire rope. --- SCIENCE / Mechanics / Dynamics --- MATHEMATICS / Applied