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Journal articles on the topic 'Lagrangian equations of motion'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Garcia-Sucre, M., U. Percoco, and L. Núñez. "An example of a general class of symmetries of Lagrangians and their equations of motion." Canadian Journal of Physics 69, no. 10 (1991): 1217–20. http://dx.doi.org/10.1139/p91-182.

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Results on symmetries of equations of motion and equivalent Lagrangians are applied to obtain constants of motion of the two-dimensional isotropic and anisotropic oscillators. We find that the anisotropic case provides the first example of a general kind of Lagrangian symmetries.

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2

Wang, T., and D. Kohli. "Closed and Expanded Form of Manipulator Dynamics Using Lagrangian Approach." Journal of Mechanisms, Transmissions, and Automation in Design 107, no. 2 (1985): 223–25. http://dx.doi.org/10.1115/1.3258712.

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An alternative derivation of the equations of motion of a chain of rigid bodies using Lagrangian equations of motion is presented. In an effort to reduce the complexity of the coefficients appearing in the equations of motion, a modified form of Lagrangian equations due to Silver [3] are utilized. This approach leads to a simplified form of coefficients of the equation of motion.

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3

Hajihashemi, Mahdi, and Ahmad Shirzad. "A generalized model for the classical relativistic spinning particle." International Journal of Modern Physics A 31, no. 07 (2016): 1650027. http://dx.doi.org/10.1142/s0217751x16500275.

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Following the Poincaré algebra, in the Hamiltonian approach, for a free spinning particle and using the Casimirs of the algebra, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the Lagrangian given in the literature. We analyze the dynamics of this generalized system in the Lagrangian formulation and show that the equations of motion support an oscillatory solution corresponding to the spinning nature of the system. Then we analyze the canonical structure of the system and present the correct gauge suitable for the spinning motion of the s

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4

Parsa, Kourosh. "THE LAGRANGIAN DERIVATION OF KANE’S EQUATIONS." Transactions of the Canadian Society for Mechanical Engineering 31, no. 4 (2007): 407–20. http://dx.doi.org/10.1139/tcsme-2007-0029.

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The Lagrangian approach to the development of dynamics equations for a multi-body system, constrained or otherwise, requires solving the forward kinematics of the system at velocity level in order to derive the kinetic energy of the system. The kinetic-energy expression should then be differentiated multiple times to derive the equations of motion of the system. Among these differentiations, the partial derivative of kinetic energy with respect to the system generalized coordinates is specially cumbersome. In this paper, we will derive this partial derivative using a novel kinematic relation f

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5

Udwadia, F. E., and R. E. Kalaba. "Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints." Journal of Applied Mechanics 68, no. 3 (2000): 462–67. http://dx.doi.org/10.1115/1.1364492.

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Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of

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6

Dreisigmeyer, David W., and Peter M. Young. "Nonconservative Lagrangian Mechanics: Purely Causal Equations of Motion." Foundations of Physics 45, no. 6 (2015): 661–72. http://dx.doi.org/10.1007/s10701-015-9892-7.

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7

YAKUBOVICH, E. I., and D. A. ZENKOVICH. "Matrix approach to Lagrangian fluid dynamics." Journal of Fluid Mechanics 443 (September 25, 2001): 167–96. http://dx.doi.org/10.1017/s0022112001005195.

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A new approach to ideal-fluid hydrodynamics based on the notion of continuous deformation of infinitesimal material elements is proposed. The matrix approach adheres to the Lagrangian (material) view of fluid motion, but instead of Lagrangian particle trajectories, it treats the Jacobi matrix of their derivatives with respect to Lagrangian variables as the fundamental quantity completely describing fluid motion.A closed set of governing matrix equations equivalent to conventional Lagrangian equations is formulated in terms of this Jacobi matrix. The equation of motion is transformed into a non

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8

Fogarasy, A. A., and M. R. Smith. "A unified tensor approach to the analysis of mechanical systems." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 211, no. 4 (1997): 313–22. http://dx.doi.org/10.1243/0954406971522079.

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It is shown in this paper that all methods of dynamic analysis of mechanisms used in practice can be derived from an invariant formed from the Lagrangian equation of motion. For the dynamic analysis of mechanisms subjected to kinematic constraint conditions, the Lagrangian equations of motion are far more suitable than the Newtonian approach. Since the Lagrangian equations are tensor equations, they are valid irrespective of what kind of generalized coordinates are used. This is not so, however, when the Newtonian approach is used. It is demonstrated by a simple example that a careless use of

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9

Burdík, Č., V. K. Pandey, and A. Reshetnyak. "BRST–BFV and BRST–BV descriptions for bosonic fields with continuous spin on R1,d−1." International Journal of Modern Physics A 35, no. 26 (2020): 2050154. http://dx.doi.org/10.1142/s0217751x20501547.

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Gauge-invariant descriptions for a free bosonic scalar field of continuous spin in a [Formula: see text]-dimensional Minkowski space–time using a metric-like formulation are constructed on the basis of a constrained BRST–BFV approach we propose. The resulting BRST–BFV equations of motion for a scalar field augmented by ghost operators contain different sets of auxiliary fields, depending on the manner of a partial gauge-fixing and a resolution of some of the equations of motion for a BRST-unfolded first-stage reducible gauge theory. To achieve an equivalence of the resulting BRST-unfolded cons

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10

Jarabah, Ola. "Action Function Formulation for Conservative Systems with Second-Order Lagrangian." Applied Physics Research 10, no. 4 (2018): 50. http://dx.doi.org/10.5539/apr.v10n4p50.

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The Euler Lagrange equation is studied to obtain the equations of motion for conservative systems with second order Lagrangian. The solutions of these equations are substituted in the given Lagrangian. The action function is then derived by calculating the time integral of the Lagrangian. To explain the application of our formalism two examples are discussed.

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11

Gitman, D. M., and V. G. Kupriyanov. "Quantization of theories with non-Lagrangian equations of motion." Journal of Mathematical Sciences 141, no. 4 (2007): 1399–406. http://dx.doi.org/10.1007/s10958-007-0047-z.

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12

GUHA, PARTHA. "GENERALIZED POISSON MECHANICS IN D-BRANES." International Journal of Modern Physics A 17, no. 31 (2002): 4759–75. http://dx.doi.org/10.1142/s0217751x02012363.

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Following the work of David Fairlie and his collaborators, we discuss the geometry of the equations of motion for the companion Lagrangian. This arises while we attempt to construct the field theoretic Lagrangians for strings and branes. These equations are related to generalized Bateman equations. Interestingly, an inhomogeneous form of these equations are related to what Dubrovin and Novikov called equations of the hydrodynamic type. We translate this set of equations into (Nambu)–Poisson equations and formulate the Lax representation of these systems. We deform all this set of equations by

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13

LONGUET-HIGGINS, MICHAEL S. "Theory of water waves derived from a Lagrangian. Part 1. Standing waves." Journal of Fluid Mechanics 423 (November 3, 2000): 275–91. http://dx.doi.org/10.1017/s0022112000001919.

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A new system of equations for calculating time-dependent motions of deep-water gravity waves (Balk 1996) is here developed analytically and set in a form suitable for practical applications. The method is fully nonlinear, and has the advantage of essential simplicity. Both the potential and the kinetic energy involve polynomial expressions of low degree in the Fourier coefficients Yn(t). This leads to equations of motion of correspondingly low degree. Moreover the constants in the equations are very simple. In this paper the equations of motion are specialized to standing waves, where the coef

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14

BHATTACHARYYA, RAJSEKHAR, and DEBASHIS GANGOPADHYAY. "DUALITY IN EQUATIONS OF MOTION FROM SPACE–TIME DEPENDENT LAGRANGIANS." Modern Physics Letters A 15, no. 14 (2000): 901–11. http://dx.doi.org/10.1142/s0217732300000906.

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Starting from Lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit space–time dependence of the Lagrangian. Poincaré invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both Abelian and non-Abelian dualities. We illustrate how (a) Dirac string solution, (b) Dirac quantization condition, (c) 't Hooft–Polyakov monopole solutions and (d) a procedure emerges for obtaining new classical solutions of Yang–Mills (YM) theory

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15

Tort, Marine, and Thomas Dubos. "Usual Approximations to the Equations of Atmospheric Motion: A Variational Perspective." Journal of the Atmospheric Sciences 71, no. 7 (2014): 2452–66. http://dx.doi.org/10.1175/jas-d-13-0339.1.

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Abstract The usual geophysical approximations are reframed within a variational framework. Starting from the Lagrangian of the fully compressible Euler equations expressed in a general curvilinear coordinates system, Hamilton’s principle of least action yields Euler–Lagrange equations of motion. Instead of directly making approximations in these equations, the approach followed is that of Hamilton’s principle asymptotics; that is, all approximations are performed in the Lagrangian. Using a coordinate system where the geopotential is the third coordinate, diverse approximations are considered.

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16

El-Nabulsi, R. A. "Nonstandard fractional exponential Lagrangians, fractional geodesic equation, complex general relativity, and discrete gravity." Canadian Journal of Physics 91, no. 8 (2013): 618–22. http://dx.doi.org/10.1139/cjp-2013-0145.

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Nonstandard Lagrangians are generating functions of different equations of motion. They have gained increasing importance in many different fields. In fact, nonstandard Lagrangians date back to 1978, when Arnold entitled them “non-natural” in his classic book, Mathematical Methods of Classical Mechanics (Springer, New York. 1978). In applied mathematics, most dynamical equations can be obtained by using generating Lagrangian functions (e.g., power-law and exponential Lagrangians), which has been shown by mathematicians, who have also demonstrated that there is an infinite number of such functi

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17

Grishchuk, L. P., and S. M. Kopejkin. "Equations of motion for isolated bodies with relativistic corrections including the radiation reaction force." Symposium - International Astronomical Union 114 (1986): 19–34. http://dx.doi.org/10.1017/s0074180900147941.

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We have derived in an explicit form the equations of motion for two spherically-symmetric non rotating bodies in the slow motion approximation. The equations include relativistic corrections of order (v/c)2, (v/c)4 and (v/c)5 to the newtonian equations of motion. It is shown that the equations depend on the only parameter characterizing each body, namely on its relativistic mass, regardless of its internal structure and degree of compactness. This means that the equations can also be applied to bodies with a strong internal gravity, such as neutron stars and black holes. It is shown that in th

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18

Cheng, Xu-Hui, and Guo-Qing Huang. "A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries." Symmetry 13, no. 4 (2021): 584. http://dx.doi.org/10.3390/sym13040584.

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In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison

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19

Pan, Ye-Chen, R. A. Scott, and A. Galip Ulsoy. "Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints." Journal of Mechanical Design 112, no. 3 (1990): 307–14. http://dx.doi.org/10.1115/1.2912609.

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A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into

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20

TURAKULOV, ZAFAR, and MARGARITA SAFONOVA. "MOTION OF A VECTOR PARTICLE IN A CURVED SPACETIME I: LAGRANGIAN APPROACH." Modern Physics Letters A 18, no. 08 (2003): 579–85. http://dx.doi.org/10.1142/s0217732303009113.

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The equations of motion for a particle with spin are derived from a simple Lagrangian. The spin is shown to be conserved on the particle's worldline. In the absence of a spin the equation coincides with that of a geodesic. The equations of motion are valid for massless particles as well, since mass does not enter the equations explicitly.

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21

Udwadia, Firdaus E., and Aaron D. Schutte. "Equations of motion for general constrained systems in Lagrangian mechanics." Acta Mechanica 213, no. 1-2 (2010): 111–29. http://dx.doi.org/10.1007/s00707-009-0272-2.

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22

CRASMAREANU, MIRCEA, and IULIAN STOLERIU. "NONHOLONOMIC DYNAMICS OF SECOND ORDER AND THE HEISENBERG SPINNING PARTICLE." International Journal of Geometric Methods in Modern Physics 09, no. 07 (2012): 1220010. http://dx.doi.org/10.1142/s0219887812200101.

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The equations of motion for the associated constrained Lagrangian to a nonholonomic Lagrangian of second order are computed. The spinning particle subject to the Heisenberg constraint is treated as example and its dynamics is completely described.

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23

VOLOVICH, I. V. "AFFINE STRINGS." Modern Physics Letters A 08, no. 19 (1993): 1827–34. http://dx.doi.org/10.1142/s0217732393001550.

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A new model of bosonic strings is considered. An action of the model is the sum of the standard string action and a term describing an interaction of a metric with a linear (affine) connection. The Lagrangian of this interaction is an arbitrary analytic function f(R) of the scalar curvature. This is a classically integrable model. The space of classical solutions of the theory consists of sectors with constant curvature. In each sector the equations of motion reduce to the standard string equations and to an additional constant curvature equation for the linear connection. A bifurcation in the

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24

OLSON, JAMES A., and RICHARD J. KEREKES. "The motion of fibres in turbulent flow." Journal of Fluid Mechanics 377 (December 25, 1998): 47–64. http://dx.doi.org/10.1017/s0022112098002973.

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Equations of mean and fluctuating velocities in rotation and translation have been derived for rigid thin inertialess fibres moving in a turbulent fluid. The derived equations for mean motion are general to fluid velocities that vary nonlinearly along the length of the fibre. From the equations of fluctuating fibre velocity, rotational and translational dispersion coefficients were derived. The resulting dispersion coefficients were shown to decrease as the ratio of fibre length to Lagrangian integral length scale of the turbulence increased.

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25

McKeon, D. G. C. "Classical motion of a point particle with extrinsic curvature." Canadian Journal of Physics 69, no. 7 (1991): 830–32. http://dx.doi.org/10.1139/p91-136.

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We consider the classical motion of a point particle whose Lagrangian involves not only the usual arc length, but also the extrinsic curvature associated with its trajectory. This Lagrangian is independent of the parameterization used to characterize the trajectory; by choosing this parameter to be the time coordinate associated with the position of the particle in space-time, we obtain a Lagrangian dependent on the position, velocity, and acceleration of the particle in a co-moving frame. Some special solutions to the Hamiltonian equations of motion are presented for the case of the free part

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26

Valelis, Christos, Fotios K. Anagnostopoulos, Spyros Basilakos, and Emmanuel N. Saridakis. "Building healthy Lagrangian theories with machine learning." International Journal of Modern Physics D 30, no. 11 (2021): 2150085. http://dx.doi.org/10.1142/s0218271821500851.

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The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of new physical theories using machine learning is possible. Specifically, we utilize a fully-connected, feed-forward neural network architecture, aiming to discriminate between “healthy” and “nonhealthy” Lagrangians, without explicitly extracting the relevant equations of motion. The network, after training, is used as a fitness function in the concept of a gen

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27

Samokhvalov, S., and A. Hryshchenko. "THE LAWS OF MOTION IN GAUGE THEORIES OF GRAVITY." Collection of scholarly papers of Dniprovsk State Technical University (Technical Sciences) 1, no. 38 (2021): 116–22. http://dx.doi.org/10.31319/2519-2884.38.2021.14.

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The general theory of relativity (GR) states that the matter that generates the gravitational field cannot move arbitrarily, it must obey certain equations that follow from the equations of the gravitational field as conditions for their compatibility. In this article we analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Object: to consider the laws of motion in gauge theories of gravitation. Task to analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Con

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28

Popescu, Paul, and Marcela Popescu. "On a cotangent form of a nonholonomic lagrangian dynamics." ITM Web of Conferences 34 (2020): 03012. http://dx.doi.org/10.1051/itmconf/20203403012.

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A Lagrangian form of dynamic equations for nonlinear nonholonomic constraints was studied by the ﬁrst author in a previous paper. The aim of this paper is to put these equations in a cotangent form, according to some regularity conditions. It is particularized as an example to a decelerated motion of a free particle, when some dual simple equations are obtained.

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29

LOZINSKI, ALEXEI, and MICHEL V. ROMERIO. "MOTION OF GAS BUBBLES, CONSIDERED AS MASSLESS BODIES, AFFORDING DEFORMATIONS WITHIN A PRESCRIBED FAMILY OF SHAPES, IN AN INCOMPRESSIBLE FLUID UNDER THE ACTION OF GRAVITATION AND SURFACE TENSION." Mathematical Models and Methods in Applied Sciences 17, no. 09 (2007): 1445–78. http://dx.doi.org/10.1142/s0218202507002340.

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A model allowing to describe motion and coalescence of gas bubbles in a liquid under the action of gravitation and surface tension is proposed. The shape of the bubbles is described by a pre-defined family of mappings, for example ellipsoids with a fixed volume and the effects of the gas motions inside the bubbles are neglected. The motion of a bubble is obtained in a Lagrangian form using the D'Alembert principle of virtual works. The set of equations is numerically solved with the help of the fictitious domain technique in which the Navier–Stokes equations in the domain formed by both fluid

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30

Fu, Jing-Li, Lijun Zhang, Chaudry Khalique, and Ma-Li Guo. "Motion equations and non-Noether symmetries of Lagrangian systems with conformable fractional derivative." Thermal Science 25, no. 2 Part B (2021): 1365–72. http://dx.doi.org/10.2298/tsci200520035f.

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In this paper, we present the fractional motion equations and fractional non-Noether symmetries of Lagrangian systems with the conformable fractional derivatives. The exchanging relationship between isochronous variation and fractional derivative, and the fractional Hamilton?s principle of the holonomic conservative and non-conservative systems under the conformable fractional derivative are proposed. Then the fractional motion equations of these systems based on the Hamil?ton?s principle are established. The fractional Euler operator, the definition of fractional non-Noether symmetries, non-N

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31

POL'SHIN, S. A. "A SIMPLE VARIATIONAL PRINCIPLE FOR CLASSICAL SPINNING PARTICLE WITH ANOMALOUS MAGNETIC MOMENTUM." Modern Physics Letters A 24, no. 05 (2009): 331–33. http://dx.doi.org/10.1142/s0217732309030138.

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32

Enferadi, Javad, and Mohammad Tavakolian. "Lagrangian Dynamics Analysis of a XY-Theta Parallel Robotic Machine Tool." Periodica Polytechnica Mechanical Engineering 61, no. 2 (2017): 107. http://dx.doi.org/10.3311/ppme.9368.

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Dynamics of a highly stiff parallel machine tool is the subject of this paper. High stiffness, good accuracy, relatively large workspace and free of singularities on the whole workspace makes the manipulator suitable for machining applications as an XY-Theta precision table. First, obtaining kinematics constraints, inverse kinematics analysis and velocity analysis are performed. Next, using six redundant generalized coordinates, we obtain Lagrangian of the manipulator. Also, a Lagrangian approach is proposed to obtain dynamics equations of the machine tool using three Lagrangian multipliers. T

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33

Ciaglia, F. M., F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, and A. Zampini. "Lagrangian description of Heisenberg and Landau–von Neumann equations of motion." Modern Physics Letters A 35, no. 19 (2020): 2050161. http://dx.doi.org/10.1142/s0217732320501618.

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An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau–von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state.

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34

Biolek, Zdenek, Dalibor Biolek, and Viera Biolkova. "Lagrangian for Circuits with Higher-Order Elements." Entropy 21, no. 11 (2019): 1059. http://dx.doi.org/10.3390/e21111059.

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The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R 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. If all the elemen

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35

Aycan, Cansel, and Simge Şimşek. "Time-Dependent Lagrangian Energy Systems on Supermanifolds with Graph Bundles." Journal of Mathematics 2021 (April 28, 2021): 1–17. http://dx.doi.org/10.1155/2021/5528123.

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The aim of this article is firstly to improve time-dependent Lagrangian energy equations using the super jet bundles on supermanifolds. Later, we adapted this study to the graph bundle. Thus, we created a graph bundle by examining the graph manifold structure in superspace. The geometric structures obtained for the mechanical energy system with superbundle coordinates were reexamined with the graph bundle coordinates. Thus, we were able to calculate the energy that occurs during the motion of a particle when we examine this motion with graph points. The supercoordinates on the superbundle stru

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36

Athanassoulis, G. A., and T. A. Loukakis. "Lagrangian Expressions of the Hydrodynamic Forces Acting on a Rigid Body in the Presence of a Free Surface." Journal of Ship Research 29, no. 01 (1985): 12–22. http://dx.doi.org/10.5957/jsr.1985.29.1.12.

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The formalism of classical analytical dynamics is used in conjunction with the principle of virtual velocity to derive Lagrangian expressions for the hydrodynamic forces acting on a rigid body moving through an in-viscid and incompressible liquid with a free surface. Simultaneously, a corresponding Lagrangian expression is derived for the hydrodynamic pressure acting on the free surface itself. The expressions for the hydrodynamic forces degenerate to the classical ones if the free surface is not present, and the expression for the pressure is reduced to that obtained by Milder if the rigid bo

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37

Sharapov, A. A. "Peierls brackets in non-Lagrangian field theory." International Journal of Modern Physics A 29, no. 27 (2014): 1450157. http://dx.doi.org/10.1142/s0217751x14501577.

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The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson bracket on the space of solutions to the classical equations of motion, be they Lagrangian or not. The bracket generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.

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Battista, Emmanuele, Giampiero Esposito, Luciano Di Fiore, Simone Dell’Agnello, Jules Simo, and Aniello Grado. "On solar system dynamics in general relativity." International Journal of Geometric Methods in Modern Physics 14, no. 09 (2017): 1750117. http://dx.doi.org/10.1142/s0219887817501171.

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Recent work in the literature has advocated using the Earth–Moon–planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the curren

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Heinz, Stefan. "Nonlinear Lagrangian equations for turbulent motion and buoyancy in inhomogeneous flows." Physics of Fluids 9, no. 3 (1997): 703–16. http://dx.doi.org/10.1063/1.869421.

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40

Volavy, Jaroslav, Árpád Farkas, Frantisek Lizal, Jakub Elcner, and Miroslav Jicha. "Lagrangian tracking of fibres in a channel flow." EPJ Web of Conferences 213 (2019): 02098. http://dx.doi.org/10.1051/epjconf/201921302098.

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Tracking of fibres in a fluid flow is much more complicated than tracking of spherical particles. In fibre motion, the orientation of fibre against the flow direction plays a very important role. In addition to the standard equation of motion, additional equations for orientation and angular velocity must be solved during the tracking of fibres. A mathematical model describing fibre motion is introduced in this work. Capabilities of this model are demonstrated through simulations of fibre transportation by air in a channel flow. The importance of the terms in the equation of angular velocity a

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Rabei, Eqab M., and Mohammed Al Horani. "Quantization of fractional singular Lagrangian systems using WKB approximation." International Journal of Modern Physics A 33, no. 36 (2018): 1850222. http://dx.doi.org/10.1142/s0217751x18502226.

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In this paper, the fractional singular Lagrangian system is studied. The Hamilton–Jacobi treatment is developed to be applicable for fractional singular Lagrangian system. The equations of motion are obtained for the fractional singular systems and the Hamilton–Jacobi partial differential equations are obtained and solved to determine the action integral. Then the wave function for fractional singular system is obtained. Besides, to demonstrate this theory, the fractional Christ-Lee model is discussed and quantized using the WKB approximation.

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HARKO, TIBERIU, TOMI S. KOIVISTO, and FRANCISCO S. N. LOBO. "PALATINI FORMULATION OF MODIFIED GRAVITY WITH A NON-MINIMAL CURVATURE-MATTER COUPLING." Modern Physics Letters A 26, no. 20 (2011): 1467–80. http://dx.doi.org/10.1142/s0217732311035869.

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We derive the field equations and the equations of motion for scalar fields and massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi–Cività connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the nonconservation of the energy–momentum tensor. We derive the explicit form of the equations of

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CARDOSO, J. G. "COMPLEXIFIED THEORY OF POSITIVE-FREQUENCY MAXWELL-DIRAC FIELDS." International Journal of Modern Physics A 08, no. 21 (1993): 3697–719. http://dx.doi.org/10.1142/s0217751x93001508.

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We present a method whereby the equations of motion yielding the explicit two-component spinor form of the complete Maxwell-Dirac theory in complex Minkowski space may be directly derived from two variational principles. One of these dynamical statements gives rise to the first half of the electromagnetic theory which particularly appears as the equations of motion involving a slightly modified version of the free part of the conventional Maxwell Lagrangian density. The other principle actually involves a holomorphic two-spinor expression for the full Maxwell-Dirac Lagrangian density which lea

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BABOUROVA, O. V., and B. N. FROLOV. "PERFECT HYPERMOMENTUM FLUID: VARIATIONAL THEORY AND EQUATIONS OF MOTION." International Journal of Modern Physics A 13, no. 31 (1998): 5391–407. http://dx.doi.org/10.1142/s0217751x98002444.

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The variational theory of the perfect hypermomentum fluid is developed. The new type of the generalized Frenkel condition is considered. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid and the Weyssenhoff-type evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the canonical energy–momentum three-form, the metric stress–energy four-form and the hypermomentum three-form) are obtained. The Euler-type hydrodynamic equation of motion of the perfect hypermomentum fluid is derived. It is proved that

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GIMÉNEZ, ÁNGEL. "RELATIVISTIC PARTICLES ALONG NULL CURVES IN 3D LORENTZIAN SPACE FORMS." International Journal of Bifurcation and Chaos 20, no. 09 (2010): 2851–59. http://dx.doi.org/10.1142/s0218127410027404.

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We study relativistic particles modeled by actions whose Lagrangians are arbitrary functions on the curvature of null paths in (2 + 1)-dimensions backgrounds with constant curvature. We obtain first integrals of the Euler–Lagrange equation by using geometrical methods involving the search for Killing vector fields along critical curves of the action. In the case in which Lagrangian density depends quadratically on Cartan curvature, it is shown that the mechanical system is governed by a stationary Korteweg–De Vries system. Motion equations are completely integrated by quadratures in terms of e

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DERIGLAZOV, A. A. "VARIATIONAL PROBLEM FOR THE FRENKEL AND THE BARGMANN–MICHEL–TELEGDI (BMT) EQUATIONS." Modern Physics Letters A 28, no. 01 (2013): 1250234. http://dx.doi.org/10.1142/s0217732312502343.

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We propose Lagrangian formulation for the particle with value of spin fixed within the classical theory. The Lagrangian is invariant under non-Abelian group of local symmetries. On this reason, all the initial spin variables turn out to be unobservable quantities. As the gauge-invariant variables for description of spin we can take either the Frenkel tensor or the Bargmann–Michel–Telegdi (BMT) vector. Fixation of spin within the classical theory implies O(ℏ)-corrections to the corresponding equations of motion.

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CAMCI, UGUR. "DIRAC ANALYSIS AND INTEGRABILITY OF GEODESIC EQUATIONS FOR CYLINDRICALLY SYMMETRIC SPACETIMES." International Journal of Modern Physics D 12, no. 08 (2003): 1431–44. http://dx.doi.org/10.1142/s0218271803003621.

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Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of motion are integrated, and found some solutions for Lewis, Levi-Civita, and Van Stockum spacetimes.

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Nagarajan, S., and D. A. Turcic. "Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part II—System Equations." Journal of Dynamic Systems, Measurement, and Control 112, no. 2 (1990): 215–24. http://dx.doi.org/10.1115/1.2896128.

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The first step in the derivation of the equations of motion for general elastic mechanism systems was described in Part I of this work. The equations were derived at the elemental level using Lagrange’s equation and the generalized coordinates were both the rigid body degrees of freedom, and the elastic degrees of freedom of element ‘e’. Each rigid body degree of freedom gave rise to a scalar equation of motion, and the elastic degrees of freedom of element e gave rise to a vector equation of motion. Since both the rigid body degrees of freedom and elastic degrees of freedom are considered as

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Scholle, M., and F. Marner. "A non-conventional discontinuous Lagrangian for viscous flow." Royal Society Open Science 4, no. 2 (2017): 160447. http://dx.doi.org/10.1098/rsos.160447.

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Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics

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MUNNIER, ALEXANDRE. "ON THE SELF-DISPLACEMENT OF DEFORMABLE BODIES IN A POTENTIAL FLUID FLOW." Mathematical Models and Methods in Applied Sciences 18, no. 11 (2008): 1945–81. http://dx.doi.org/10.1142/s021820250800325x.

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Understanding fish-like locomotion as a result of internal shape changes may result in improved underwater propulsion mechanism. In this paper, we study a coupled system of partial differential equations and ordinary differential equations which models the motion of self-propelled deformable bodies (called swimmers) in a potential fluid flow. The deformations being prescribed, we apply the least action principle of Lagrangian mechanics to determine the equations of the inferred motion. We prove that the swimmers' degrees of freedom solve a second-order system of nonlinear ordinary differential

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