2017, First edition., ISBN 0198743041, xii, 267 pages

This book is about 'action' and the Principle of Least Action. These ideas are at the heart of physical science and engineering...

Least action | Mathematical physics | Physical science

Least action | Mathematical physics | Physical science

Book

International journal for numerical methods in engineering, ISSN 0029-5981, 09/2010, Volume 83, Issue 10, pp. 1273 - 1311

...‐field. In this paper, we outline a thermodynamically consistent framework for phase‐field models of crack propagation in elastic solids, develop incremental variational principles and consider their numerical implementations by multi...

crack propagation | incremental variational principles | phase‐fields | coupled multi‐field problems | gradient‐type damage | finite elements | fracture | Finite elements | Incremental variationalprinciples | Coupled multi-field problems | Phase-fields | Fracture | Gradient-type damage | Crack propagation | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology

crack propagation | incremental variational principles | phase‐fields | coupled multi‐field problems | gradient‐type damage | finite elements | fracture | Finite elements | Incremental variationalprinciples | Coupled multi-field problems | Phase-fields | Fracture | Gradient-type damage | Crack propagation | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology

Journal Article

03/2018, ISBN 9780521869027, 270

The principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path...

Lagrange equations | Mechanics | Hamilton-Jacobi equations | Variational principles | Least action

Lagrange equations | Mechanics | Hamilton-Jacobi equations | Variational principles | Least action

eBook

Journal of solid state chemistry, ISSN 0022-4596, 10/2009, Volume 182, Issue 10, pp. 2664 - 2669

The structural properties, heats of formation, elastic properties, and electronic structures of Al–Ni intermetallic compounds are analyzed here in detail by...

Mechanical properties | Nickel aluminides | Heats of formation | Electrical properties | First-principle electron theory | Multi-materials systems | Physical Sciences | Chemistry, Inorganic & Nuclear | Chemistry | Chemistry, Physical | Science & Technology | Intermetallic compounds | Analysis | FORMATION HEAT | THERMODYNAMIC PROPERTIES | DENSITY FUNCTIONAL METHOD | CALCULATION METHODS | MONOCRYSTALS | TRANSITION ELEMENT ALLOYS | ELECTRICAL PROPERTIES | MATERIALS SCIENCE | ELECTRONIC STRUCTURE | VARIATIONAL METHODS | ELASTICITY | ENTHALPY | ALUMINIUM ALLOYS | ALLOYS | PHYSICAL PROPERTIES | CRYSTALS | MECHANICAL PROPERTIES | NICKEL ALLOYS | POLYCRYSTALS | INTERMETALLIC COMPOUNDS | REACTION HEAT

Mechanical properties | Nickel aluminides | Heats of formation | Electrical properties | First-principle electron theory | Multi-materials systems | Physical Sciences | Chemistry, Inorganic & Nuclear | Chemistry | Chemistry, Physical | Science & Technology | Intermetallic compounds | Analysis | FORMATION HEAT | THERMODYNAMIC PROPERTIES | DENSITY FUNCTIONAL METHOD | CALCULATION METHODS | MONOCRYSTALS | TRANSITION ELEMENT ALLOYS | ELECTRICAL PROPERTIES | MATERIALS SCIENCE | ELECTRONIC STRUCTURE | VARIATIONAL METHODS | ELASTICITY | ENTHALPY | ALUMINIUM ALLOYS | ALLOYS | PHYSICAL PROPERTIES | CRYSTALS | MECHANICAL PROPERTIES | NICKEL ALLOYS | POLYCRYSTALS | INTERMETALLIC COMPOUNDS | REACTION HEAT

Journal Article

Acta mechanica, ISSN 1619-6937, 11/2019, Volume 231, Issue 2, pp. 625 - 647

The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting...

Mechanics | Technology | Science & Technology | Rods | Variational principles | Mathematical analysis | Differential geometry

Mechanics | Technology | Science & Technology | Rods | Variational principles | Mathematical analysis | Differential geometry

Journal Article

1966, Interscience monographs and texts in physics and astronomy, v. 20, x, 310

Book

Physics of plasmas, ISSN 1089-7674, 09/2014, Volume 21, Issue 9, p. 092118

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving...

Physical Sciences | Physics, Fluids & Plasmas | Physics | Science & Technology | FLUIDS | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY | PLASMA | SYMMETRY | APPROXIMATIONS | ELECTRONS | EQUATIONS OF MOTION | HAMILTONIANS | MAGNETOHYDRODYNAMICS | PLASMA EXPANSION | VARIATIONAL METHODS

Physical Sciences | Physics, Fluids & Plasmas | Physics | Science & Technology | FLUIDS | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY | PLASMA | SYMMETRY | APPROXIMATIONS | ELECTRONS | EQUATIONS OF MOTION | HAMILTONIANS | MAGNETOHYDRODYNAMICS | PLASMA EXPANSION | VARIATIONAL METHODS

Journal Article

International journal for numerical methods in engineering, ISSN 0029-5981, 06/2018, Volume 114, Issue 11, pp. 1192 - 1212

Summary
Two variational principles are proposed that describe equilibrium problems with connected nonlinear beams and solids...

variational methods | interface element | warping | nonlinear beam | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology | Finite element method | Potential energy | Deformation | Lagrange multipliers | Mathematical analysis | Principles | Kinematics | Formability | Variational principles

variational methods | interface element | warping | nonlinear beam | Mathematics, Interdisciplinary Applications | Engineering | Physical Sciences | Technology | Engineering, Multidisciplinary | Mathematics | Science & Technology | Finite element method | Potential energy | Deformation | Lagrange multipliers | Mathematical analysis | Principles | Kinematics | Formability | Variational principles

Journal Article

Journal of physics. Condensed matter, ISSN 1361-648X, 07/2011, Volume 23, Issue 28, pp. 284118 - 8

...) extended Rayleigh's principle of the least energy dissipation to general irreversible processes...

Models, Theoretical | Thermodynamics | Liquid Crystals - chemistry | Models, Chemical | Hydrodynamics | Gels - chemistry | Kinetics | Viscoelastic Substances | Physics | Irreversible processes | Condensed matter | Energy dissipation | Mathematical analysis | Phase separation | Nonlinearity | Mathematical models | Variational principles | Index Medicus

Models, Theoretical | Thermodynamics | Liquid Crystals - chemistry | Models, Chemical | Hydrodynamics | Gels - chemistry | Kinetics | Viscoelastic Substances | Physics | Irreversible processes | Condensed matter | Energy dissipation | Mathematical analysis | Phase separation | Nonlinearity | Mathematical models | Variational principles | Index Medicus

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 04/2011, Volume 56, Issue 4, pp. 913 - 917

.... This provides an analog of Pontryagin's maximum principle for single-input Boolean networks.

systems biology | Biological system modeling | Switches | needle variation | variational analysis | Switched systems | Boolean functions | Logical functions | Optimal control | necessary condition for optimality | sum of products representation | Matrix converters | semi-tensor product | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Systems biology | Algebra, Boolean | Analysis | Networks | Cellular communication | Automatic control | Genetics | Maximum principle | Mathematical models | Boolean algebra | Optimization

systems biology | Biological system modeling | Switches | needle variation | variational analysis | Switched systems | Boolean functions | Logical functions | Optimal control | necessary condition for optimality | sum of products representation | Matrix converters | semi-tensor product | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Systems biology | Algebra, Boolean | Analysis | Networks | Cellular communication | Automatic control | Genetics | Maximum principle | Mathematical models | Boolean algebra | Optimization

Journal Article

Chaos, solitons and fractals, ISSN 0960-0779, 09/2017, Volume 102, pp. 94 - 98

We obtain Euler–Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on...

Fractional variational principles | Herglotz problem | Generalized fractional operators | Euler–Lagrange equations | Mathematics, Interdisciplinary Applications | Physical Sciences | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Physics | Science & Technology

Fractional variational principles | Herglotz problem | Generalized fractional operators | Euler–Lagrange equations | Mathematics, Interdisciplinary Applications | Physical Sciences | Physics, Mathematical | Physics, Multidisciplinary | Mathematics | Physics | Science & Technology

Journal Article

Applied Physics Letters, ISSN 0003-6951, 03/2011, Volume 98, Issue 11, pp. 112104 - 112104-3

...
-Fe
2
O
3
were studied via the first-principles calculations with density function theory
(
DFT
)
+
U
method...

Physical Sciences | Physics | Science & Technology | Physics, Applied | OXYGEN COMPOUNDS | CALCULATION METHODS | HYDROGEN COMPOUNDS | ENERGY RANGE | TRANSITION ELEMENTS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | IONS | ELECTRICAL PROPERTIES | MAGNETIC MATERIALS | COPPER | ENERGY LEVELS | SOLAR ENERGY | IRON OXIDES | TRANSITION ELEMENT COMPOUNDS | COMPUTERIZED SIMULATION | DENSITY | ELEMENTS | PHOTOELECTROCHEMICAL CELLS | METALS | CHARGED PARTICLES | PHYSICAL PROPERTIES | DOPED MATERIALS | HYDROGEN PRODUCTION | IRON ORES | WATER | ENERGY | OXIDE MINERALS | MINERALS | DENSITY FUNCTIONAL METHOD | FERRIMAGNETIC MATERIALS | ELECTROCHEMICAL CELLS | EV RANGE | IRON | FERRITES | TITANIUM | ENERGY SOURCES | SIMULATION | ENERGY GAP | VARIATIONAL METHODS | CHALCOGENIDES | HEMATITE | ORES | RENEWABLE ENERGY SOURCES | IRON-ALPHA | OXIDES | ELECTRIC CONDUCTIVITY | MATERIALS | IRON COMPOUNDS

Physical Sciences | Physics | Science & Technology | Physics, Applied | OXYGEN COMPOUNDS | CALCULATION METHODS | HYDROGEN COMPOUNDS | ENERGY RANGE | TRANSITION ELEMENTS | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | IONS | ELECTRICAL PROPERTIES | MAGNETIC MATERIALS | COPPER | ENERGY LEVELS | SOLAR ENERGY | IRON OXIDES | TRANSITION ELEMENT COMPOUNDS | COMPUTERIZED SIMULATION | DENSITY | ELEMENTS | PHOTOELECTROCHEMICAL CELLS | METALS | CHARGED PARTICLES | PHYSICAL PROPERTIES | DOPED MATERIALS | HYDROGEN PRODUCTION | IRON ORES | WATER | ENERGY | OXIDE MINERALS | MINERALS | DENSITY FUNCTIONAL METHOD | FERRIMAGNETIC MATERIALS | ELECTROCHEMICAL CELLS | EV RANGE | IRON | FERRITES | TITANIUM | ENERGY SOURCES | SIMULATION | ENERGY GAP | VARIATIONAL METHODS | CHALCOGENIDES | HEMATITE | ORES | RENEWABLE ENERGY SOURCES | IRON-ALPHA | OXIDES | ELECTRIC CONDUCTIVITY | MATERIALS | IRON COMPOUNDS

Journal Article

Physical review letters, ISSN 1079-7114, 03/2011, Volume 106, Issue 11, pp. 112502 - 112502

The Balian-Veneroni (BV) variational principle, which optimizes the evolution of the state according to the relevant observable, is used at the mean-field level...

Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Nuclear Theory | VARIATIONS | APPROXIMATIONS | CALCULATION METHODS | FERMIONS | NUCLEAR REACTIONS | CORRELATIONS | STABLE ISOTOPES | LEPTON-HADRON INTERACTIONS | MEAN-FIELD THEORY | DIRECT REACTIONS | TIME DEPENDENCE | ALKALINE EARTH ISOTOPES | LIGHT NUCLEI | SCATTERING | CALCIUM ISOTOPES | NEUTRONS | CALCIUM 40 | MANY-BODY PROBLEM | LEPTON-BARYON INTERACTIONS | EVEN-EVEN NUCLEI | LEPTON-NUCLEON INTERACTIONS | INTERACTIONS | PROTONS | ELEMENTARY PARTICLES | VARIATIONAL METHODS | NUCLEONS | HARTREE-FOCK METHOD | ISOTOPES | NUCLEAR PHYSICS AND RADIATION PHYSICS | NUCLEI | TRANSFER REACTIONS | FLUCTUATIONS | PARTICLE INTERACTIONS | INELASTIC SCATTERING | DEEP INELASTIC SCATTERING | BARYONS | HADRONS

Physics, Multidisciplinary | Physical Sciences | Physics | Science & Technology | Nuclear Theory | VARIATIONS | APPROXIMATIONS | CALCULATION METHODS | FERMIONS | NUCLEAR REACTIONS | CORRELATIONS | STABLE ISOTOPES | LEPTON-HADRON INTERACTIONS | MEAN-FIELD THEORY | DIRECT REACTIONS | TIME DEPENDENCE | ALKALINE EARTH ISOTOPES | LIGHT NUCLEI | SCATTERING | CALCIUM ISOTOPES | NEUTRONS | CALCIUM 40 | MANY-BODY PROBLEM | LEPTON-BARYON INTERACTIONS | EVEN-EVEN NUCLEI | LEPTON-NUCLEON INTERACTIONS | INTERACTIONS | PROTONS | ELEMENTARY PARTICLES | VARIATIONAL METHODS | NUCLEONS | HARTREE-FOCK METHOD | ISOTOPES | NUCLEAR PHYSICS AND RADIATION PHYSICS | NUCLEI | TRANSFER REACTIONS | FLUCTUATIONS | PARTICLE INTERACTIONS | INELASTIC SCATTERING | DEEP INELASTIC SCATTERING | BARYONS | HADRONS

Journal Article

Automatica (Oxford), ISSN 0005-1098, 09/2016, Volume 71, pp. 78 - 88

...–d’Alembert principle from variational mechanics. With body-fixed vision and inertial sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation error and the sum...

Lie group variational integrator | Pose estimation | Variational estimator | Lagrange–d’Alembert principle | Lagrange-d'Alembert principle | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Numerical analysis | Sensors | Analysis | Measuring instruments | Force and energy | Aerospace engineering

Lie group variational integrator | Pose estimation | Variational estimator | Lagrange–d’Alembert principle | Lagrange-d'Alembert principle | Engineering, Electrical & Electronic | Engineering | Automation & Control Systems | Technology | Science & Technology | Numerical analysis | Sensors | Analysis | Measuring instruments | Force and energy | Aerospace engineering

Journal Article

2014, Mechanical engineering and solid mechanics series, ISBN 1848216793, Volume 9781848216792, 424

...: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics...

Viscoelasticity | Calculus | Mathematical models | Waves | Fractional calculus | Mechanics

Viscoelasticity | Calculus | Mathematical models | Waves | Fractional calculus | Mechanics

eBook

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 12/2011, Volume 44, Issue 49, pp. 495402 - 30

We provide Vasiliev's fully nonlinear equations of motion for bosonic higher spin gauge fields in four spacetime dimensions with an action principle...

Physics, Multidisciplinary | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Equivalence | Lagrange multipliers | Mathematical analysis | Mathematical models | Spectra | Variational principles | Equations of motion | Gages | Gauges | Physics - High Energy Physics - Theory

Physics, Multidisciplinary | Physical Sciences | Physics | Physics, Mathematical | Science & Technology | Equivalence | Lagrange multipliers | Mathematical analysis | Mathematical models | Spectra | Variational principles | Equations of motion | Gages | Gauges | Physics - High Energy Physics - Theory

Journal Article