Radioengineering, ISSN 1210-2512, 06/2017, Volume 26, Issue 2, pp. 397 - 405

The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua's periodic table...

Higher-order elements | Action | FDNR | Lagrangian | Energy | Periodic table of fundamental elements | Content | Evolution | Dissipation function | Inerter | higher-order elements | dissipation function | inerter | action | evolution | content | energy | ENGINEERING, ELECTRICAL & ELECTRONIC

Higher-order elements | Action | FDNR | Lagrangian | Energy | Periodic table of fundamental elements | Content | Evolution | Dissipation function | Inerter | higher-order elements | dissipation function | inerter | action | evolution | content | energy | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2010, Volume 92, Issue 3, pp. 221 - 229

We obtain several Euler–Lagrange equations for variational functionals defined on a set of Hölder curves...

Geometry | 39A12 | scale calculus | non-differentiability | Theoretical, Mathematical and Computational Physics | Euler–Lagrange equations | 26B05 | Group Theory and Generalizations | higher-order scale derivatives | Statistical Physics, Dynamical Systems and Complexity | 49K05 | Physics | Higher-order scale derivatives | Non-differentiability | Scale calculus | Euler-Lagrange equations | PHYSICS, MATHEMATICAL | RELATIVITY

Geometry | 39A12 | scale calculus | non-differentiability | Theoretical, Mathematical and Computational Physics | Euler–Lagrange equations | 26B05 | Group Theory and Generalizations | higher-order scale derivatives | Statistical Physics, Dynamical Systems and Complexity | 49K05 | Physics | Higher-order scale derivatives | Non-differentiability | Scale calculus | Euler-Lagrange equations | PHYSICS, MATHEMATICAL | RELATIVITY

Journal Article

ENTROPY, ISSN 1099-4300, 11/2019, Volume 21, Issue 11, p. 1059

...+ types minus the sum of the state functions of the elements of the C or R- types. The equations of motion generated by this Lagrangian are always of even-order...

Chua's table | TABLE | Lagrangian | PHYSICS, MULTIDISCIPLINARY | memristor | EQUATIONS | NETWORKS | Hamilton's variational principle | higher-order element | Euler-Lagrange equation | lagrangian | chua’s table | euler–lagrange equation | hamilton’s variational principle

Chua's table | TABLE | Lagrangian | PHYSICS, MULTIDISCIPLINARY | memristor | EQUATIONS | NETWORKS | Hamilton's variational principle | higher-order element | Euler-Lagrange equation | lagrangian | chua’s table | euler–lagrange equation | hamilton’s variational principle

Journal Article

UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, ISSN 1223-7027, 2009, Volume 71, Issue 2, pp. 3 - 18

... out. The Euler-Lagrange equations for different types of variables in Osc(k) M are given; they are coordinate invariant, and have different forms for k = 21 and for k = 21+1...

Homogeneity | Lagrangians and Hamiltonians of higher order | Euler-Lagrange equations | Legendre transformation | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY

Homogeneity | Lagrangians and Hamiltonians of higher order | Euler-Lagrange equations | Legendre transformation | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2014, Volume 410, Issue 2, pp. 733 - 749

We consider systems of Euler–Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities...

Equivalence | Differential invariant | Euler–Lagrange equations | Euler-Lagrange equations | MATHEMATICS | MATHEMATICS, APPLIED | EQUIVALENCE PROBLEM | SYMMETRIES | CLASSIFICATION | HIGHER-ORDER LAGRANGIANS

Equivalence | Differential invariant | Euler–Lagrange equations | Euler-Lagrange equations | MATHEMATICS | MATHEMATICS, APPLIED | EQUIVALENCE PROBLEM | SYMMETRIES | CLASSIFICATION | HIGHER-ORDER LAGRANGIANS

Journal Article

6.
Full Text
Noether currents for higher-order variational problems of Herglotz type with time delay

Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 02/2018, Volume 11, Issue 1, pp. 91 - 102

We study, from an optimal control perspective, Noether currents for higher-order problems of Herglotz type with time delay. Main result provides new Noether...

Higher-order problems | Noether’s theorems | Optimal control | Euler–Lagrange equations | Retarded systems | Herglotz’s variational problems | Invariance | Currents | Euler Lagrange equations | currents | MATHEMATICS, APPLIED | higher-order problems | SYMMETRY THEOREM | Herglotz's variational problems | optimal control | invariance | PRINCIPLE | retarded systems | Noether's theorems

Higher-order problems | Noether’s theorems | Optimal control | Euler–Lagrange equations | Retarded systems | Herglotz’s variational problems | Invariance | Currents | Euler Lagrange equations | currents | MATHEMATICS, APPLIED | higher-order problems | SYMMETRY THEOREM | Herglotz's variational problems | optimal control | invariance | PRINCIPLE | retarded systems | Noether's theorems

Journal Article

7.
Full Text
Optimality conditions for the calculus of variations with higher-order delta derivatives

Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 1, pp. 87 - 92

We prove the Euler–Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals...

Arbitrary time scales | Euler–Lagrange equation | Higher-order delta derivatives | Calculus of variations | EulerLagrange equation | MATHEMATICS, APPLIED | ISOPERIMETRIC PROBLEMS | TIME SCALES | Euler-Lagrange equation | Derivatives (Financial instruments) | Deltas | Derivatives | Functionals | Mathematical analysis | Optimization | Mathematics - Optimization and Control

Arbitrary time scales | Euler–Lagrange equation | Higher-order delta derivatives | Calculus of variations | EulerLagrange equation | MATHEMATICS, APPLIED | ISOPERIMETRIC PROBLEMS | TIME SCALES | Euler-Lagrange equation | Derivatives (Financial instruments) | Deltas | Derivatives | Functionals | Mathematical analysis | Optimization | Mathematics - Optimization and Control

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2015, Volume 48, Issue 20, pp. 1 - 32

...) Lagrangian or Hamiltonian, as well as the Euler-Lagrange equations. As important examples, we geometrically derive the classical higher order Euler-Lagrange equations...

Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles

Higher order Lagrangians | Tulczyjew triple | Graded bundle | Geometrical mechanics | graded bundle | higher order Lagrangians | AV-DIFFERENTIAL GEOMETRY | POISSON | PHYSICS, MULTIDISCIPLINARY | LIE ALGEBROIDS | MANIFOLDS | PHYSICS, MATHEMATICAL | geometrical mechanics | LAGRANGIAN MECHANICS | Euler-Lagrange equation | Mathematical analysis | Formalism | Invariants | Bundles

Journal Article

Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 14, pp. 1201 - 1211

.... This is done in relation to higher-order Euler–Lagrange equations and a Hamiltonian framework...

Higher order Euler–Lagrange equation | Pais–Uhlenbeck oscillators | Discontinuous velocity jumps | Newton's second law of motion | Nonlocal-in-time kinetic energy | Quantized nonlocality time extent | Higher order Euler-Lagrange equation | Pais-Uhlenbeck oscillators | PHYSICS, MULTIDISCIPLINARY | QUANTUM | LAGRANGIANS | EQUATIONS | GRAVITY | MECHANICS | MOTION | SYSTEMS | HIGHER DERIVATIVES | QUANTIZATION | CLOCK | Force and energy

Higher order Euler–Lagrange equation | Pais–Uhlenbeck oscillators | Discontinuous velocity jumps | Newton's second law of motion | Nonlocal-in-time kinetic energy | Quantized nonlocality time extent | Higher order Euler-Lagrange equation | Pais-Uhlenbeck oscillators | PHYSICS, MULTIDISCIPLINARY | QUANTUM | LAGRANGIANS | EQUATIONS | GRAVITY | MECHANICS | MOTION | SYSTEMS | HIGHER DERIVATIVES | QUANTIZATION | CLOCK | Force and energy

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 2/2014, Volume 21, Issue 1, pp. 1 - 26

...Nonlinear Diﬀer. Equ. Appl. 21 (2014), 1–26 c null2013 Springer Basel 1021-9722/14/010001-26 published online May 3, 2013 Nonlinear Diﬀerential Equations DOI...

49k24 | 90C31 | Approximation | 49J52 | Analysis | 49k 20 | Multivalued | Mathematics | Higher order | Transversality | 49M25 | Euler–Lagrange | Euler-Lagrange | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | MAPPINGS | OPTIMALITY

49k24 | 90C31 | Approximation | 49J52 | Analysis | 49k 20 | Multivalued | Mathematics | Higher order | Transversality | 49M25 | Euler–Lagrange | Euler-Lagrange | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | MAPPINGS | OPTIMALITY

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2019, Volume 182, Issue 3, pp. 965 - 983

...$$ S n following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler...

53B21 | 49S05 | Variational problems of Herglotz type | Mathematics | Theory of Computation | Higher-order optimal control problems | 34H05 | Higher-order variational problems | Optimization | Euclidean sphere | Riemannian cubic polynomials | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49K15 | SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | THEOREM | PRINCIPLE | FORMULATION | BIRKHOFFIAN SYSTEM | Riemann manifold | Polynomials | Euler-Lagrange equation | Mathematical analysis | Optimal control

53B21 | 49S05 | Variational problems of Herglotz type | Mathematics | Theory of Computation | Higher-order optimal control problems | 34H05 | Higher-order variational problems | Optimization | Euclidean sphere | Riemannian cubic polynomials | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49K15 | SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | THEOREM | PRINCIPLE | FORMULATION | BIRKHOFFIAN SYSTEM | Riemann manifold | Polynomials | Euler-Lagrange equation | Mathematical analysis | Optimal control

Journal Article

Zeitschrift für Naturforschung A, ISSN 0932-0784, 09/2016, Volume 71, Issue 9, pp. 817 - 821

In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens’s nonlocal-in-time kinetic energy approach, which is motivated...

Higher-Order Euler-Lagrange Equations | Nonlocal in Space-Time | Generalized Klein-Gordon and Dirac Equations | Spinor Field | 03.50.-z | 04.30.Xx | Nonlocal-in-Time Kinetic Energy | Nonlocalin- Time Kinetic Energy | DERIVATION | MECHANICS | PHYSICS, MULTIDISCIPLINARY | FIELD | DYNAMICS | CHEMISTRY, PHYSICAL | STOCHASTIC QUANTIZATION | Usage | Algebra | Kinetic energy | Differential equations, Partial | Analysis | Dirac equation

Higher-Order Euler-Lagrange Equations | Nonlocal in Space-Time | Generalized Klein-Gordon and Dirac Equations | Spinor Field | 03.50.-z | 04.30.Xx | Nonlocal-in-Time Kinetic Energy | Nonlocalin- Time Kinetic Energy | DERIVATION | MECHANICS | PHYSICS, MULTIDISCIPLINARY | FIELD | DYNAMICS | CHEMISTRY, PHYSICAL | STOCHASTIC QUANTIZATION | Usage | Algebra | Kinetic energy | Differential equations, Partial | Analysis | Dirac equation

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 10/2017, Volume 43, Issue 5, pp. 1163 - 1195

.... Conditions are derived that ensure the linear independence of the higher order constrained discrete Euler-Lagrange equations and stiff accuracy...

Visualization | Computational Mathematics and Numerical Analysis | 65P10 | Mathematical and Computational Biology | Mathematics | Higher order integration | Symplectic momentum methods | Computational Science and Engineering | 70Hxx | Numerical convergence analysis | 70F20 | 65L80 | Mathematical Modeling and Industrial Mathematics | Variational integrators | Time reversibility | Holonomic constraints | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | HAMILTONIAN-SYSTEMS | INDEX-3 | Analysis | Numerical analysis

Visualization | Computational Mathematics and Numerical Analysis | 65P10 | Mathematical and Computational Biology | Mathematics | Higher order integration | Symplectic momentum methods | Computational Science and Engineering | 70Hxx | Numerical convergence analysis | 70F20 | 65L80 | Mathematical Modeling and Industrial Mathematics | Variational integrators | Time reversibility | Holonomic constraints | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | HAMILTONIAN-SYSTEMS | INDEX-3 | Analysis | Numerical analysis

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 05/2013, Volume 33, Issue 5, pp. 1987 - 2005

This paper is concerned with the symmetry results for the 2k-order singular Lane-Emden type partial differential system {(-Delta)(k)(vertical bar x vertical...

Weighted Hardy-Littlewood-Sobolev inequality | Higher-order Lane-Emden system | Method of moving planes | Axisymmetry | axisymmetry | MATHEMATICS, APPLIED | BEHAVIOR | INTEGRAL-EQUATIONS | CLASSIFICATION | weighted Hardy-Littlewood-Sobolev inequality | SPACE | MATHEMATICS | method of moving planes | SYMMETRY | THEOREMS | ELLIPTIC-EQUATIONS

Weighted Hardy-Littlewood-Sobolev inequality | Higher-order Lane-Emden system | Method of moving planes | Axisymmetry | axisymmetry | MATHEMATICS, APPLIED | BEHAVIOR | INTEGRAL-EQUATIONS | CLASSIFICATION | weighted Hardy-Littlewood-Sobolev inequality | SPACE | MATHEMATICS | method of moving planes | SYMMETRY | THEOREMS | ELLIPTIC-EQUATIONS

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 01/2017, Volume 41, pp. 494 - 507

....•The proper adhesive functions for satisfying boundary conditions are proposed.•A modified Euler–Lagrange equation based on CPT is obtained and then solved...

Functionally graded circular plate | Higher order shear deformation theory | Spectral Ritz method | Buckling | Pasternak elastic foundation | Euler–Lagrange | VIBRATION | STABILITY | VARIABLE THICKNESS | Euler-Lagrange | FGM PLATES | SANDWICH PLATES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | Analysis | Differential equations

Functionally graded circular plate | Higher order shear deformation theory | Spectral Ritz method | Buckling | Pasternak elastic foundation | Euler–Lagrange | VIBRATION | STABILITY | VARIABLE THICKNESS | Euler-Lagrange | FGM PLATES | SANDWICH PLATES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | Analysis | Differential equations

Journal Article

ENTROPY, ISSN 1099-4300, 04/2020, Volume 22, Issue 4, p. 412

The paper studies the construction of the Hamiltonian for circuits built from the (alpha,beta) elements of Chua's periodic table. It starts from the Lagrange...

Chua's table | Lagrangian | PHYSICS, MULTIDISCIPLINARY | memristor | constitutive relation | higher-order element | Euler-Lagrange equation | Hamiltonian | EULER-LAGRANGE EQUATIONS | Chua’s table

Chua's table | Lagrangian | PHYSICS, MULTIDISCIPLINARY | memristor | constitutive relation | higher-order element | Euler-Lagrange equation | Hamiltonian | EULER-LAGRANGE EQUATIONS | Chua’s table

Journal Article

17.
Optimization of lagrange problem with higher order differential inclusions and endpoint constraints

Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 7, pp. 2367 - 2382

.... The sufficient conditions of optimality containing the Euler-Lagrange and Hamiltonian type inclusions as a result of endpoint constraints are accompanied by so-called "endpoint" conditions...

Euler-Lagrange | Higher order | Euler-Poisson | Set-valued | Hamiltonian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | SUFFICIENT CONDITIONS | higher order | DISCRETE | set-valued

Euler-Lagrange | Higher order | Euler-Poisson | Set-valued | Hamiltonian | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | SUFFICIENT CONDITIONS | higher order | DISCRETE | set-valued

Journal Article

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, ISSN 1578-7303, 3/2012, Volume 106, Issue 1, pp. 89 - 95

.... This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle...

Secondary 70H50 | Vakonomic constraints | 55R10 | Theoretical, Mathematical and Computational Physics | Euler–Lagrange equations | Mathematics, general | Mathematics | Higher order field theory | Applications of Mathematics | Multisymplectic form | Primary 70S05 | 53C80 | Euler-Lagrange equations | MATHEMATICS | ALGORITHM

Secondary 70H50 | Vakonomic constraints | 55R10 | Theoretical, Mathematical and Computational Physics | Euler–Lagrange equations | Mathematics, general | Mathematics | Higher order field theory | Applications of Mathematics | Multisymplectic form | Primary 70S05 | 53C80 | Euler-Lagrange equations | MATHEMATICS | ALGORITHM

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 12/2015, Volume 194, Issue 6, pp. 1835 - 1858

...–Lagrange equation, and we give lower bounds for $$\Lambda _{1,1}^c(\Omega...

46E35 | 49J52 | Minimization problem | Higher order Sobolev embeddding | Mathematics, general | Mathematics | 35P30 | Clamped 1-biharmonic operator | Faber-Krahn type inequality | 35G15 | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | RAYLEIGHS CONJECTURE | Analysis of PDEs

46E35 | 49J52 | Minimization problem | Higher order Sobolev embeddding | Mathematics, general | Mathematics | 35P30 | Clamped 1-biharmonic operator | Faber-Krahn type inequality | 35G15 | EIGENVALUE | MATHEMATICS | MATHEMATICS, APPLIED | RAYLEIGHS CONJECTURE | Analysis of PDEs

Journal Article

Bulletin of the Brazilian Mathematical Society, New Series, ISSN 1678-7544, 12/2011, Volume 42, Issue 4, pp. 579 - 606

... reduction, Euler-Lagrange equations, Euler-Poincaré equations, Lagrange-Poincaré equations, Hamilton-Poincaré equations. Mathematical subject classification: 70H50...

37J15 | Theoretical, Mathematical and Computational Physics | Poisson brackets | Mathematics | Hamilton-Poincaré equations | Lagrange-Poincaré equations | Euler-Poincaré equations | 70H25 | variational principle | 70H30 | symmetry | Lie-Poisson reduction | Euler-Lagrange equations | 70H50 | Mathematics, general | connection | higher order tangent bundle | Mathematical Physics | General Mathematics | Physics

37J15 | Theoretical, Mathematical and Computational Physics | Poisson brackets | Mathematics | Hamilton-Poincaré equations | Lagrange-Poincaré equations | Euler-Poincaré equations | 70H25 | variational principle | 70H30 | symmetry | Lie-Poisson reduction | Euler-Lagrange equations | 70H50 | Mathematics, general | connection | higher order tangent bundle | Mathematical Physics | General Mathematics | Physics

Journal Article

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