You are not logged in! Please log in to edit your catalogs. About this series Titles in this series. Driven by increasingly elaborate modern technological applications, the symbolic relationship between mathematics and mechanics is continually growing. Mechanics is understood here in the most general sense of the word, including, besides its standard interpretation, relevant physical, biological, and information theoretical phenomena, such as electromagnetic, thermal and quantum effects, bio- and nano-mechanics, information geometry, multiscale modelling, neural networks, computation, optimization and control of complex systems, etc.

Topics with multi-disciplinary range, such as duality, complementarity, and symmetry in sciences and mathematics, are of particular interest. The often-used term body needs to stand for a wide assortment of objects, including particles, projectiles , spacecraft , stars , parts of machinery , parts of solids , parts of fluids gases and liquids , etc. Other distinctions between the various sub-disciplines of mechanics, concern the nature of the bodies being described.

Particles are bodies with little known internal structure, treated as mathematical points in classical mechanics. Rigid bodies have size and shape, but retain a simplicity close to that of the particle, adding just a few so-called degrees of freedom , such as orientation in space.

Otherwise, bodies may be semi-rigid, i. These subjects have both classical and quantum divisions of study. For instance, the motion of a spacecraft, regarding its orbit and attitude rotation , is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.

Note that there is also the " theory of fields " which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether classical fields or quantum fields. But in actual practice, subjects belonging to mechanics and fields are closely interwoven. Thus, for instance, forces that act on particles are frequently derived from fields electromagnetic or gravitational , and particles generate fields by acting as sources. In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the wave function.

The following are categorized as being part of quantum mechanics :. From Wikipedia, the free encyclopedia. This article is about an area of scientific study. For other uses, see Mechanic disambiguation. Second law of motion. History Timeline. Newton's laws of motion. Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton—Jacobi equation Appell's equation of motion Udwadia—Kalaba equation Koopman—von Neumann mechanics.

Core topics. Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed. Classical mechanics Old quantum theory Bra—ket notation Hamiltonian Interference. Advanced topics. Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory quantum mechanics Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics.

Main articles: History of classical mechanics and History of quantum mechanics. Main article: Aristotelian mechanics. Main article: Theory of impetus. Play media. A History of Classical Mechanics. Classical Mechanics. West Petal Nagar, New Delhi. Tata McGraw-Hill, , pg 6. The University of Texas at Austin. Physics Education. Bibcode : PhyEd.. The Islamic intellectual tradition in Persia. Annals of the New York Academy of Sciences.

Annals of the New York Academy of Sciences vol. Review of jet and rocket engine technologies. Jet and rocket engine thermodynamic and aerodynamic principles. Performance of turbojet, turbofan, and turboprop jet engines. Rocket engines include liquid, cryogenic, solid, and electric propulsion. Probabilistic design of mechanical components and systems. Reliability functions, hazard models and product life prediction. Theoretical stress-strength-time models.

Static and dynamic reliability models. Optimum design of mechanical systems for reliability objectives or constraints. Advanced topics in mechanical systems design. Kinematics and dynamics of planar machinery. Shock and vibration control in machine elements.

Balancing of rotating and reciprocating machines.

- Strength of Materials | Review;
- The Art of Modeling in Computational Solid Mechanics!
- Mechanics & Materials!
- Poincare seminar 2010: Chaos.

Design projects using commercial computer-aided-engineering software for the design and evaluation of typical machine systems. Dynamic analysis of mechanical, electromechanical, fluid and hybrid engineering systems with emphasis on the modeling process. Lumped and distributed-parameter models. Use of computer tools for modeling, design and simulation. Design projects. A comprehensive course in classical and modern linear control systems. Includes root locus, frequency response, state space, and digital control techniques with extensive use of computational methods.

A design project provides experience with practical design issues and tradeoffs.

Impact of computer-aided engineering tools on mechanical design and analysis. Part geometry modeling and assembly modeling using solid representations.

## Navigation

Analysis for mass properties, interference, kinematics, displacements, stresses and system dynamics by using state-of-the-art commercially available computer-aided-engineering software. Integrated design projects. A study of some field of mechanical engineering not covered elsewhere. Consent of department chair required. The forces and moments acting on rigid aircraft are developed from basic aerodynamics and used to determine the equations of motion and the resulting dynamic models.

Analysis from these dynamic models supports the design of flight control, guidance, and autopilot systems.

## Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics - CRC Press Book

Modern control methods for missiles and spacecraft are also included. Undergraduate course assumes rigid airplane structures, while the graduate course develops the effects of flexible structures. Systems engineering approach to design, integration, testing, and operations of spacecraft for various missions. Technologies currently used in modern spacecraft bus and payload systems, astrodynamics, launch systems, life-cycle costs, and operational issues. Team works to design a spacecraft that meets a specific set of mission requirements. A consideration of the engineering problems related to nuclear reactor design and operation.

Topics include fundamental properties of atomic and nuclear radiation, reactor fuels and materials, reactor design and operation, thermal aspects, safety and shielding, instrumentation and control. Course includes several design projects stressing the major topics in the course. Must have senior standing in engineering or physical science.

Structure of the nucleus. Quantum theory. Nuclear energy release: Fission vs. Plasma for fusion. Power balances in fusion plasmas. Magnetic and inertial confinement fusion concepts. Magnetic equilibrium configurations and limitations. The Tokamak. Emerging and alternative concepts. Fusion reactor economics. Radiation sources and Radioactive decay. Interactions of radiation with matter, detectors and protection from radiation. Energy deposition and dose calculations. Applications in dosimetry, imaging and spectroscopy.

Fundamentals and design aspects of Renewable Energy RE technologies; biofuels, hydropower, solar photovoltaic, solar thermal, wind, geothermal energies.

### The Art of Modeling in Computational Solid Mechanics

Details and difficulties in implementing RE. Senior standing in Engineering. Effect of coal properties on plant performance.

Design and performance of coal-based electric power generation systems. Technologies to control emissions. Carbon capture and sequestration methods for coal-fired power plants and analysis of CCS options. Must have junior standing in engineering or physical science. Studies of the plant operation and energy usage. Students work with the Lehigh Industrial Assessment Center to do technical and economic feasibility studies of optimizing energy consumption. Industrial experience. Fundamentals of best practices to save energy, reduce waste, and increase productivity.

Consent of instructor required. Experiments and applications utilizing combinations of mechanical, electrical, and microprocessor components. Theory and application of electronic and electromechanical equipment, operation and control of mechatronic systems. Projects integrating mechanical, electronic and microcontrollers. Energy usage and supply, fossil fuel technologies, renewable energy alternatives and environmental impacts.

The scope will be broad to give some perspective of the problems, but in-depth technical analysis of many aspects will also be developed. Polymer processes such as injection molding through a combination of theory development, practical analysis, and utilization of commercial software. Polymer chemistry and structure, material rheological behavior, processing kinetics, molecular orientation development, process simulation software development, manufacturing defects, manufacturing window establishment, manufacturing process design, manufacturing process optimization.

Must have senior level standing in engineering or science. Sampled-data systems; z-transforms; pulse transfer functions; stability in the z-plane; root locus and frequency response design methods; minimal prototype design; digital control hardware; discrete state variables; state transition matrix; Liapunov stability state feedback control two lectures and one laboratory per week.

Opportunity for Eckardt Scholars to pursue an extended project for senior honors. Transcript will identify department in which project was completed. Experiments on a variety of mechanical, electrical and chemical dynamic control systems. Exposure to state-of-the-art control instrumentation: sensors, transmitters, control valves, analog and digital controllers. Emphasis on design of feedback controllers and comparison of theoretical computer simulation predictions with actual experimental data. Lab teams will be interdisciplinary. An integrated and interdisciplinary approach to engineering design, concurrent engineering, design for manufacturing, industrial design and the business of new product development.

Topics include design methods, philosophy and practice, the role of modeling and simulation, decision making, risk, cost, material and manufacturing process selection, platform and modular design, mass customization, quality, planning and scheduling, business issues, teamwork, group dynamics, creativity and innovation. The course uses case studies and team projects.

The course focuses on the fundamental science-base underlying manufacturing processes, and applying that science base to develop knowledge and tools suitable for industrial utilization. Selected manufacturing processes representing the general classes of material removal, material deformation, material phase change, material flow, and material joining are addressed. Students create computer-based process simulation tools independently as well as utilize leading commercial process simulation packages.

Laboratory experiences are included throughout the course. The course is intended as a first graduate course in viscous flow. An introduction to boundary-layer theory, thermodynamics and heat transfer at the undergraduate level are assumed to have been completed.

Topics include the fundamental equation of continuum fluid mechanics, the concept of asymptotic methods and low and high Reynolds number flows, laminar boundary layers, generalized similarity methods, two-and three-dimensional flows, steady and unsteady flows and an introduction to hydrodynamic stability. The material is covered in the context of providing a logical basis as an introduction to a further course in turbulent flows.

Zeros of functions, difference tables, interpolation, integration, differentiation. Divided differences, numerical solution of ordinary differential equations of the boundary and initial value type. Eigen problems. Curve fitting, matrix manipulation and solution of linear algebraic equations. Partial differential equations of the hyperbolic, elliptic and parabolic type. Application to problems in mechanical engineering. Excitation of streamlined- and bluff-bodies by self-excited, vortex, turbulence, and gust-excitation mechanisms.

Analogous excitation of fluid compressible and free-surface systems having rigid boundaries. Extensive case studies. Critical review of thermodynamics systems. Criteria for equilibrium. Applications to electromagnetic systems. Statistical thermodynamics.

### 1.1 Introduction

Irreversible thermodynamics. Thermoelectric phenomena. Emphasis on theoretical and experimental treatment of combustion processes including dissociation, flame temperature calculations, diffusion flames, stability and propagation; related problems in compressible flow involving one-dimensional, oblique shock waves and detonation waves. Methods of measurement and instrumentation. This course is a first graduate course in the basic concepts of heat and mass transfer, providing a broad coverage of key areas in diffusion, conduction, convection, heat and mass transfer, and radiation.

Topics covered include: the conservation equations, steady and transient diffusion and conduction, periodic diffusion, melting and solidification problems, numerical methods, turbulent convection, transpiration and film cooling, free convection, heat transfer with phase change, heat exchanges, radiation, mixed mode heat and mass transfer. Stability of laminar flow; transition to turbulence. Navier-Stokes equations with turbulence. Bounded turbulent shear flows; free shear flows; statistical description of turbulence. Principles of radiative transfer; thermal-radiative properties of diffuse and specular surfaces; radiative exchange between bodies; radiative transport through absorbing, emitting and scattering media.

Advanced topics in steady-state and transient conduction; analytical and numerical solutions; problems of combined conductive and radiative heat transfer. Navier-Stokes and energy equations, laminar boundary layer theory, analysis of friction drag, transfer and separation. Transition from laminar to turbulent flow.

Turbulent boundary layer theory. Prandtl mixing length, turbulent friction drag, and heat transfer. Integral methods. Flow in ducts, wakes and jets. Natural convection heat transfer. This course is a first graduate course in incompressible fluid mechanics, providing a broad coverage of key areas of viscous and inviscid fluid mechanics.

Topics covered include: Flow kinematics, differential equations of motion, viscous and inviscid solutions, vorticity dynamics and circulation, vorticity equation, circulation theorems, potential flow behavior, irrotational and rotational flows, simple boundary layer flows and solutions, and real fluid flows and consequences. Method of characteristics. Unsteady continuous flow. Unsteady flows with discontinuities. Shock tubes. Detonation waves. Two-dimensional and axisymmetric supersonic flows. Momentum and energy equation of compressible viscous fluids.

This course covers the following topics in linear systems and control theory: review of fundamental concepts in linear algebra, state-space representation of linear systems, linearization, time-variance and linearity properties of systems, impulse response, transfer functions and their state-space representations, solution to LTI and LTV state equations, Jordan form, Lyapunov stability, input-output stability, controllability, stabilizability, observability, detectability, Canonical forms, minimal realizations, introduction to optimal control theory, Linear Quadratic Regulator LQR , Algebraic Riccati Equation ARE , frequency domain properties of LQR controllers.

A state-of-the-art review of multivariable methods of interest to process control applications. Design techniques examined include loop interaction analysis, frequency domain methods Inverse Nyquist Array, Characteristic Loci and Singular Value Decomposition feed forward control, internal model control and dynamic matrix control.

## Advances Mechanics Mathematics

Special attention is placed on the interaction of process design and process control. Most of the above methods are used to compare the relative performance of intensive and extensive variable control structures.

The determination of model parameters from time-history and frequency response data by graphical, deterministic and stochastic methods. Examples and exercises taken from process industries, communications and aerospace testing. Regression, quasilinearization and invariant-imbedding techniques for nonlinear system parameter identification included. Linear and nonlinear models for stochastic systems. Controllability and observability. Minimum variance state estimation. Linear quadratic Gausian control problem.

Computational considerations. Nonlinear control problem in stochastic systems. Fundamental concepts of strain measurements and application of strain gages and strain gage circuits. Use of image analysis in data acquisition and interpretation. Selected laboratory experiments. Design of mechanical engineering systems to reliability specifications. Probabilistic failure models for mechanical components. Methods for the analysis and improvement of system reliability. Effect of component tolerance and parameter variation on system failure. Reliability testing. An intensive study of some field of mechanical engineering not covered in more general courses.

Analytical techniques relevant to the engineering sciences are described. Vector spaces; eigenvalues; eigenvectors. Linear ordinary differential equations; diagonalizable and non-diagonalizable systems. Inhomogeneous linear systems; variation of parameters. Non-linear systems; stability; phase plane. Series solutions of linear ordinary differential equations; special functions. Laplace and Fourier transforms; application to partial differential equations and integral equations. Sturm-Liouville theory.

Finite Fourier transforms; planar, cylindrical, and spherical geometries. Theory of complex functions; Cauchy-Riemann relations. Laurent series; singular points; contour integrals; Fourier and Laplace transforms. Evaluation of real integrals; Cauchy principal values. Singular integral equations. Classification of partial differential equations. Hyperbolic systems of partial differential equations; uniqueness, shock formation. The forces and moments acting on aircraft are developed from basic aerodynamics and used to determine the equations of motion and the resulting dynamic models.

Effects of flexible structures are developed. Modeling of complex linear and nonlinear energetic dynamic engineering systems. Emphasis on subdivision into multiport elements and representation by the bondgraph language using direct, energetic, and experimental methods.

Field lumping. Analytical and graphical reductions. Simulation and other numerical methods. Examples including mechanisms, electromechanical transducers, electric and fluid circuits, and thermal systems. Project work on some aspect of mechanical engineering in an area of student and faculty interest.

Selection and direction of the project could involve interaction with local communities or industries. Technical and economic feasibility study of new products. Selection and content of the project is determined by the faculty project advisor in consultation with the student, progress and final reports, oral and posters presentations. Consent of the program director and faculty project adviser required.

The student works with an industry sponsor to create detailed design specifications, fabricate and test a prototype new product and plan for production. Selection and content of the project is determined by the faculty project advisor in consultation with the industry sponsor. Deliverables include progress and final reports, oral presentations, posters and a prototype. Consent of the department chair and faculty project advisor required. Fundamentals and design aspects of Renewable Energy RE technologies; bio-fuels, hydropower, solar photovoltaic, solar thermal, wind, geothermal energies.

Vibration-induced acoustic radiation, wave equation in planar, cylindrical and spherical coordinates. Sound in tubes, pipes, wave guides, acoustic enclosures. Impedance and source-media-receiver transmission concepts. Noise and its measurements. Critical assessments of energy management systems. Establishment of framework for industrial facilities to manage energy systems.