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Books on the topic 'Equation statics'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

L, Daniel P., Armstrong Ernest S, and Institute for Computer Applications in Science and Engineering., eds. A spline-based parameter and static estimation technique for static models of elastic surfaces. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1987.

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2

Banks, H. Thomas. A spline-based parameter and static estimation technique for static models of elastic surfaces. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1987.

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3

Rao, Nannapaneni Narayana. Elements of engineering electromagnetics. 3rd ed. Prentice Hall, 1991.

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4

Rao, Nannapaneni Narayana. Elements of engineering electromagnetics. 4th ed. Prentice Hall, 1994.

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5

Isogai, Koji. Numerical simulation of dynamic stall of NACA0012 airfoil oscillating near static stall angle using the Navier-Stokes equations. National Aerospace Laboratory, 1992.

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6

A, Tanner John, Mason Angela J, Langley Research Center, and United States. Army Materiel Command., eds. Quasi-static viscoelastic finite element model of an aircraft tire. National Aeronautics and Space Administration, Langley Research Center, U.S. Army Materiel Command, 1999.

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7

A, Tanner John, Mason Angela J, Langley Research Center, and United States. Army Materiel Command., eds. Quasi-static viscoelastic finite element model of an aircraft tire. National Aeronautics and Space Administration, Langley Research Center, U.S. Army Materiel Command, 1999.

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8

P, Guruswamy Guru, and United States. National Aeronautics and Space Administration., eds. Convergence acceleration of a Navier-Stokes solver for efficient static aeroelastic computations. American Institute of Aeronautics and Astronautics, 1995.

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9

A, Earles James, Armstrong Laboratory (U.S.), University of Illinois at Urbana-Champaign. Dept. of Psychology., and Armstrong Laboratory (U.S.). Manpower and Personnel Research Division., eds. Air Force Officer Qualifying Test (AFOQT): Forms Q development, preliminary equating and operational equating. Air Force Materiel Command, Armstrong Laboratory, Human Resources Directorate, 1997.

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10

Center, Langley Research, ed. An approximate theoretical method for modeling the static thrust performance of non-axisymmetric two-dimensional convergent-divergent nozzles. National Aeronautics and Space Administration, Langley Research Center, 1995.

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11

Witzel, Bradley S. Solving equations: An algebra intervention. Pearson, 2010.

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12

Jr, Cobb Charles E., ed. Radical equations: Math literacy and civil rights. Beacon Press, 2001.

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13

Rosser, John Barkley, Gian Italo Bischi, L. Gardini, and Carl Chiarella. Nonlinear dynamics in economics, finance and the social sciences: Essays in honour of John Barkley Rosser Jr. Springer, 2010.

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14

Moses, Robert Parris. Radical equations: Civil rights from Mississippi to the Algebra Project. Beacon Press, 2001.

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15

Steuck, Kurt W. Air Force Officer Qualifying Test (AFOQT): Forms P pre-implementation analyses and equating. Air Force Systems Command, Air Force Human Resources Laboratory, 1988.

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16

Quenet, R. V. Site index equations for black and white spruce in northeastern B.C. and Yukon. Forestry Canada, 1989.

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17

Ahearn, Elizabeth A. Regression equations for estimating flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals in Connecticut. U.S. Geological Survey, 2004.

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18

Ahearn, Elizabeth A. Regression equations for estimating flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals in Connecticut. U.S. Geological Survey, 2004.

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19

International, Symposium in Economic Theory and Econometrics (10th 1992 Florence Italy). Nonlinear dynamics and economics: Proceedings of the Tenth International Symposium in Economic Theory and Econometrics. Cambridge University Press, 1996.

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20

Osgood, Libby, Gayla Cameron, and Emma Christensen. Engineering Mechanics: Statics. University of Prince Edward Island, 2021. http://dx.doi.org/10.32393/engnmech.

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Introduction to engineering mechanics: statics, when acceleration is 0. Concepts include: particles and rigid body equilibrium equations, distributed loads, shear and moment diagrams, trusses, method of joints and sections, & inertia. This book is intended for those who love to learn.

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21

Deruelle, Nathalie, and Jean-Philippe Uzan. Kinetic theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0010.

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This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equ

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22

Deruelle, Nathalie, and Jean-Philippe Uzan. Self-gravitating fluids. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0015.

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This chapter briefly describes ‘perfect fluids’. These are characterized by their mass density ρ‎(t, xⁱ), pressure p(t, ⁱ), and velocity field v(t, ⁱ). The motion and equilibrium configurations of these fluids are determined by the equation of state, for example, p = p(ρ‎) for a barotropic fluid, and by the gravitational potential U(t, ⁱ) created at a point ⁱ by other fluid elements. The chapter shows that, given an equation of state, the equations of the problem to be solved are the continuity equation, the Euler equation, and the Poisson equation. It then considers static models with spheric

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23

Static Green's Functions in Anisotropic Media. Cambridge University Press, 2015.

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24

Chen, Weiqiu, and Ernian Pan. Static Green's Functions in Anisotropic Media. Cambridge University Press, 2015.

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25

Chen, Weiqiu, and Ernian Pan. Static Green's Functions in Anisotropic Media. Cambridge University Press, 2015.

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26

Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

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Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is n

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27

Isett, Philip. The Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0006.

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This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechan

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28

Deruelle, Nathalie, and Jean-Philippe Uzan. The Kerr solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0048.

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This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals.

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29

T. Michaltsos, George, and Ioannis G. Raftoyiannis, eds. Bridges’ Dynamics. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/97816080522021120101.

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Bridges’ Dynamics covers the historical review of research and introductory mathematical concepts related to the structural dynamics of bridges. The e-book explains the theory behind engineering aspects such as 1) dynamic loadings, 2) mathematical concepts (calculus elements of variations, the d’ Alembert principle, Lagrange’s equation, the Hamilton principle, the equations of Heilig, and the δ and H functions), 3) moving loads, 4) bridge support mechanics (one, two and three span beams), 5) Static systems under dynamic loading 6) aero-elasticity, 7) space problems (2D and 3D) and 8) absorb sy

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30

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the

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31

Static Compression Of Energetic Materials. Springer, 2008.

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32

Escudier, Marcel. Bernoulli’s equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0007.

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In this chapter Newton’s second law of motion is used to derive Euler’s equation for the flow of an inviscid fluid along a streamline. For a fluid of constant density ρ‎ Euler’s equation can be integrated to yield Bernoulli’s equation: p + ρ‎gz′ + ρ‎V2 = pT which shows that the sum of the static pressure p, the hydrostatic pressure ρ‎gz and the dynamic pressure ρ‎V2/2 is equal to the total pressure pT. The combination p + ρ‎V2/2 is an important quantity known as the stagnation pressure. Each of the terms on the left-hand side of Bernoulli’s equation can be regarded as representing different fo

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33

Laxminarayan, Swamy. PDE and Level Sets: Algorithmic Approaches to Static and Motion Imagery. Springer London, Limited, 2006.

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34

Laxminarayan, Swamy. PDE and Level Sets: Algorithmic Approaches to Static and Motion Imagery. Springer, 2013.

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35

Maruhn, Jan H. Robust Static Super-Replication of Barrier Options. de Gruyter GmbH, Walter, 2009.

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36

Maruhn, Jan H. Robust Static Super-Replication of Barrier Options. De Gruyter, Inc., 2009.

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37

Epstein, Charles L., and Rafe Mazzeo. Holder Estimates for General Models. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0009.

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This chapter presents the Hölder estimates for general model problems. It first estimates solutions to heat equations for both the homogeneous Cauchy problem and the inhomogeneous problem, obtaining first and second derivative estimates in the latter case, before discussing a general result describing the off-diagonal and long-time behavior of the solution kernel for the general model. It also states a proposition summarizing the properties of the resolvent operator as an operator on the Hölder spaces. In contrast to the case of the heat equation, there is no need to assume that the data has c

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38

Compton scattering by static and moving media. National Aeronautics and Space Administration, 1997.

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39

Quasi-static viscoelastic finite element model of an aircraft tire. National Aeronautics and Space Administration, Langley Research Center, U.S. Army Materiel Command, 1999.

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40

Quasi-static viscoelastic finite element model of an aircraft tire. National Aeronautics and Space Administration, Langley Research Center, U.S. Army Materiel Command, 1999.

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41

PDE and level sets: Algorithmic approaches to static and motion imagery. Kluwer Academic/Plenum Publishers, 2002.

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42

Back, Kerry E. Dynamic Portfolio Choice. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0009.

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The first‐order condition for optimal portfolio choice is called the Euler equation. Optimal consumption can be computed by a static approach in a dynamic complete market and by orthogonal projection for a quadratic utility investor. Dynamic programming and the Bellman equation are explained. The envelope condition and hedging demands are explained. Investors with CRRA utility have CRRA value functions. Whether the marginal value of wealth is higher for a CRRA investor in good states or in bad states depends on whether risk aversion is less than or greater than 1. With IID returns, the optimal

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43

Rajeev, S. G. Ideal Fluid Flows. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0004.

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Some solutions of Euler’s equations are found here. The simplest are the steady flows: water flowing out of a tank at a constant rate, the Venturi and Pitot tubes. Another is the static solution of a self-gravitating fluid of variable density (e.g., a star). If the total mass is too large, such a star can collapse (Chandrasekhar limit). If the flow is both irrotational and incompressible, it must satisfy Laplace’s equation. Complex analysismethods can be used to solve for the flow past a cylinder or inside a disk with a stirrer. Joukowski used conformal transformations on the cylinder to find

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44

Antes, H. The Boundary Integral Approach to Static and Dynamic Contact Problems. Springer, 2012.

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45

(Editor), Jasjit S. Suri, and Swamy Laxminarayan (Editor), eds. PDE and Level Sets: Algorithmic Approaches to Static and Motion Imagery (Topics in Biomedical Engineering). Springer, 2002.

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46

Escudier, Marcel. Engineering applications of Bernoulli’s equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0008.

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In this chapter it is shown how Bernoulli’s equation can be applied to practical fluid-flow problems. In the case of internal flows, such as that through a Venturi tube, it is also necessary to use the continuity equation to relate changes in cross-sectional area to changes in flow velocity. For liquid flows it is shown that for sufficiently high flowspeeds the static pressure could fall below the saturated vapour pressure and lead to cavitation. The designs of various flow-measuring devices, including the orifice-plate flowmeter, the Venturi-tube flowmeter, and the Pitot tube, are based on Be

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47

Escudier, Marcel. Linear momentum equation and hydrodynamic forces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0009.

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In this chapter a method is shown for calculating the external reaction force which must be applied to a duct to counteract the hydrodynamic forces generated by a fluid flowing through it. Newton’s second law of motion applied to fluid flow through a duct of arbitrary shape leads to the linear momentum equation for fluid flow. This shows that the change in the momentum flowrate of the fluid is equal to the net force exerted on the fluid. The individual forces which contribute to the net force are the pressure forces at inlet and outlet, and the forces which arise due to the static pressure and

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48

Succi, Sauro. The Lattice Boltzmann Equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.001.0001.

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Over the past near three decades, the Lattice Boltzmann method has gained a prominent role as an efficient computational method for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales, from fully developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic subnuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this book presents a survey of the major developments w

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49

Eriksson, Olle, Anders Bergman, Lars Bergqvist, and Johan Hellsvik. The Damping Term, from First Principles. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788669.003.0006.

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In the previous chapters we described the basic principles of density functional theory, gave examples of how accurate it is to describe static magnetic properties in general, and derived from this basis the master equation for atomistic spin-dynamics; the SLL (or SLLG) equation. However, one term was not described in these chapters, namely the damping parameter. This parameter is a crucial one in the SLL (or SLLG) equation, since it allows for energy and angular momentum to dissipate from the simulation cell. The damping parameter can be evaluated from density functional theory, and the Kohn-

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50

Antes, H., and P. D. Panagiotopoulos. Boundary Integral Approach to Static and Dynamic Contact Problems: Equality and Inequality Methods. Birkhauser Verlag, 2013.

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