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Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
Mechanical engineering is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, and maintain mechanical systems. It is one of the oldest and broadest of the engineering branches.
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics.
The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models as well as model reduction. A common approach is to start from measurements of the behavior of the system and the external influences and try to determine a mathematical relation between them without going into many details of what is actually happening inside the system; this approach is called black box system identification.
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life. It has numerous applications in a wide variety of fields and disciplines, including but not limited to structural engineering, astronomy, oceanography, meteorology, hydraulics, mechanical engineering, aerospace engineering, nanotechnology, structural design, earthquake engineering, fluid dynamics, planetary sciences, and other life sciences. Connecting research between numerous disciplines, applied mechanics plays an important role in both science and engineering.
This is an alphabetical list of articles pertaining specifically to Engineering Science and Mechanics (ESM). For a broad overview of engineering, please see Engineering. For biographies please see List of engineers and Mechanicians.
Graduate Texts in Mathematics (GTM) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size. The GTM series is easily identified by a white band at the top of the book.
A parallel manipulator is a mechanical system that uses several computer-controlled serial chains to support a single platform, or end-effector. Perhaps, the best known parallel manipulator is formed from six linear actuators that support a movable base for devices such as flight simulators. This device is called a Stewart platform or the Gough-Stewart platform in recognition of the engineers who first designed and used them.
Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size.
In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear stochastic partial differential equation for the normalized density of the hidden state. In principle either approach allows one to estimate a quantity function from noisy measurements, even when the system is non-linear. The application of this approach to a specific engineering situation may be problematic however, as these equations are quite complex. The Zakai equation is a bilinear stochastic partial differential equation. It was named after Moshe Zakai.
In contact mechanics, the term unilateral contact, also called unilateral constraint, denotes a mechanical constraint which prevents penetration between two rigid/flexible bodies. Constraints of this kind are omnipresent in non-smooth multibody dynamics applications, such as granular flows, legged robot, vehicle dynamics, particle damping, imperfect joints, or rocket landings. In these applications, the unilateral constraints result in impacts happening, therefore requiring suitable methods to deal with such constraints.
In classical mechanics, analytical dynamics, also known as classical dynamics or simply dynamics, is concerned with the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies, particularly mass and moment of inertia. The foundation of modern-day dynamics is Newtonian mechanics and its reformulation as Lagrangian mechanics and Hamiltonian mechanics.
Gábor Stépán, Hungarian professor of applied mechanics, member of the Hungarian Academy of Sciences, fellow of the International Academy for Production Engineering (CIRP), fellow of the Society for Industrial and Applied Mathematics (SIAM), former dean of the Faculty of Mechanical Engineering in the Budapest University of Technology and Economics. Won the Széchenyi Prize in 2011, the Thomas K. Caughey Dynamics Award in 2015, and the Delay Systems Lifetime Achievements Award in 2021. His research fields include nonlinear vibrations, delay-differential equations, and stability theory. He was elected as a fellow of the Society for Industrial and Applied Mathematics in 2017, "for contributions to the theory and analysis of delayed dynamical systems and their applications".
Mean-field game theory is the study of strategic decision making by small interacting agents in very large populations. The use of the term "mean field" is inspired by mean-field theory in physics, which considers the behavior of systems of large numbers of particles where individual particles have negligible impacts upon the system.
Thor Inge Fossen is a Norwegian cyberneticist. Fossen received the MSc degree in Marine Technology (1987) and PhD in Engineering Cybernetics (1991) both from the Norwegian University of Science and Technology (NTNU). He is a Fulbright alumni and he pursued postgraduate studies in Aerodynamics and Aeronautics at the Department of Aeronautics and Astronautics of the University of Washington, Seattle (1989-1990). At age 28 he was appointed associated professor of guidance, navigation and control at NTNU and two years later he qualified as full professor. He has been elected member of the Norwegian Academy of Technological Sciences since 1998 and elevated to IEEE Fellow (2016) for his contributions to modeling and controlling of marine craft. Fossen is one of the founders of the company Marine Cybernetics (2002), which was acquired by DNV GL in 2014. He is co-founder of the company SCOUT Drone Inspection AS (2017) and he is involved in several new high-tech companies in Trondheim. He is currently co-director of the NTNU Center for Autonomous Marine Operations and Systems. He has made contributions in the areas of marine craft motion control systems, hydrodynamics, control theory, guidance systems and navigation.
The Robotics Toolbox is MATLAB toolbox software that supports research and teaching into arm-type and mobile robotics. While the Robotics Toolbox is free software, it requires the proprietary MATLAB environment in order to execute. A subset of functions have been ported to GNU Octave and Python. The Toolbox forms the basis of the exercises in several textbooks.
Machine learning control (MLC) is a subfield of machine learning, intelligent control and control theory which solves optimal control problems with methods of machine learning. Key applications are complex nonlinear systems for which linear control theory methods are not applicable.
Isaac Elishakoff is a Distinguished Research Professor in the Ocean and Mechanical Engineering Department in the Florida Atlantic University, Boca Raton, Florida. He is an authoritative figure in the broad area of mechanics. He has made several contributions in the areas of random vibrations, solid mechanics of composite material, semi-inverse problems of vibrations and stability, functionally graded material structures, and nanotechnology.
Igor Dmitrievich Chueshov was a Ukrainian mathematician. He was both a correspondent member of the Mathematics section of the National Academy of Sciences of Ukraine and a professor in the Department of Mathematical Physics and Computational Mathematics at the National University of Kharkiv.
References
- 1 2 3 4 "Staff Profile - Professor Reza Nakhaie". RMIT University. Retrieved 2018-06-07.
- ↑ "Nonlinear Engineering". www.degruyter.com. 2012-03-20. Retrieved 2018-06-07.
