scholarly journals On the Jacobi metric for a general Lagrangian system

2019 ◽  
Vol 60 (11) ◽  
pp. 112901
Author(s):  
Paolo Maraner
Keyword(s):  
Lagrangian System ◽  
Jacobi Metric

Mode crossing in a Lagrangian system

1978 ◽  
Vol 21 (2) ◽  
pp. 297
Author(s):  
Marshall N. Rosenbluth
Keyword(s):  
Lagrangian System

A stability theorem for dissipative magnetohydrodynamic equilibria

1982 ◽  
Vol 60 (5) ◽  
pp. 640-643 ◽  
Author(s):  
J. Teichmann
Keyword(s):  
Global Stability ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Lagrangian System ◽  
Dissipative Operators ◽  
Isentropic Flow ◽  
Liapunov Method ◽  
First Time ◽  
Two Fluid

The global stability of stationary equilibria of dissipative magnetohydrodynamics is studied using the direct Liapunov method. Sufficient conditions for stability of the linearized Euler–Lagrangian system with the full dissipative operators are given for the first time. The case of the two-fluid isentropic flow is discussed.

scholarly journals The Noether–Bessel-Hagen symmetry approach for dynamical systems

2020 ◽  
Vol 17 (14) ◽  
pp. 2050215
Author(s):  
Zbyněk Urban ◽  
Francesco Bajardi ◽  
Salvatore Capozziello
Keyword(s):  
Scalar Field ◽  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Natural Extension ◽  
Field Potential ◽  
Lagrangian System ◽  
Noether Theorem ◽  
Symmetry Approach ◽  
External Forces ◽  
Shape Of Potential

The Noether–Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the Noether–Bessel-Hagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select symmetries for a given systems. In particular, we focus on the case of harmonic oscillator as a testbed for the theory, and on a cosmological system derived from scalar–tensor gravity with unknown scalar-field potential [Formula: see text]. We show that the shape of potential is selected by the presence of symmetries. The approach results particularly useful as soon as the Lagrangian of a given system is not immediately identifiable or it is not a Lagrangian system.

scholarly journals Statistical theory of turbulence IV-Diffusion in a turbulent air stream

1935 ◽  
Vol 151 (873) ◽  
pp. 465-478 ◽  
Author(s):  
Geoffrey Ingram Taylor
Keyword(s):  
Thermal Conductivity ◽  
Statistical Theory ◽  
Line Source ◽  
Transverse Component ◽  
Lagrangian System ◽  
Principal Element ◽  
Air Stream ◽  
Heated Wire ◽  
The Mean ◽  
Statistical Theory Of Turbulence

It was pointed out in Part I that experiments on the spread of heat from a line source ( e.g ., an electrically heated wire) in a turbulent air stream may be expected to give two elements of the statistical specification of turbulence. If the spread is measured near the source the value of the mean transverse component of velocity √¯ v 2 or v ' in the notation of Part I, can be found. If the spread is examined further down-stream it should be possible to analyse the results to find the correlation function R η , which is the principal element of the representation of turbulence in the Lagrangian system. Spread of heat nearer line source Recently the spread of heat from a heated wire in a wind tunnel has been measured at points near to the source by Schubauer. The stream was made turbulent by means of grids of round bars arranged in square pattern. Their diameters were 1 /5 of the mesh length and M varied from 5 inches to 1/2 inch. The width of the heat wake was found by measuring the angle subtended at the source by the two positions where the temperature rise was half that in the centre of the wake. This angle, denoted by α, depends partly on the amount of turbulence and to a less extent on the spread of heat due to the thermal conductivity of the air. By assuming that the effect of turbulence is to communicate to the air an eddy conductivity β, which is additive to, and obeys the same law as, true thermal conductivity, a virtual angle α turb can be deduced by the relation α 2 turb = α 2 — α 2 0 ,

A Systematic Exposition of the Conservation Equations for Blast Waves

1971 ◽  
Vol 38 (4) ◽  
pp. 783-794 ◽  
Author(s):  
A. K. Oppenheim ◽  
E. A. Lundstrom ◽  
A. L. Kuhl ◽  
M. M. Kamel
Keyword(s):  
Flow Field ◽  
Blast Wave ◽  
Blast Waves ◽  
Lagrangian System ◽  
Conservation Equations ◽  
Time Profiles ◽  
Wave Coordinates ◽  
Wave Phenomena ◽  
Eulerian System ◽  
Proper Account

In order to provide a rational background for the analysis of experimental observations of blast wave phenomena, the conservation equations governing their nonsteady flow field are formulated in a general manner, without the usual restrictions imposed by an equation of state, and with proper account taken, by means of source terms, of other effects which, besides the inertial terms that conventionally dominate these equations, can affect the flow. Taking advantage of the fact that a blast wave can be generally considered as a spatially one-dimensional flow field whose nonsteady behavior can be regarded, consequently, as a function of just two independent variables, two generalized blast wave coordinates are introduced, one associated with the front of the blast wave and the other with its flow field. The conservation equations are accordingly transformed into this coordinate system, acquiring thereby a comprehensive character, in that they refer then to any frame of reference, being applicable, in particular, to problems involving either space or time profiles of the gas-dynamic parameters in the Eulerian system, or time profiles in the Lagrangian system.

scholarly journals ON THE SYMMETRIES OF HAMILTONIAN SYSTEMS

1995 ◽  
Vol 10 (04) ◽  
pp. 579-610 ◽  
Author(s):  
V. MUKHANOV ◽  
A. WIPF
Keyword(s):  
String Theory ◽  
Hamiltonian Systems ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Linear Constraints ◽  
Lagrangian System ◽  
Lagrangian Systems ◽  
Diffeomorphism Invariance ◽  
Symmetry Transformations ◽  
Local Symmetries

In this paper we show how the well-known local symmetries of Lagrangian systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta generate transformations which correspond to symmetries of the corresponding Lagrangian system. The non-linear constraints (which we have, for instance, in gravity, supergravity and string theory) generate the dynamics of the corresponding Lagrangian system. Only in a very special combination with "trivial" transformations proportional to the equations of motion do they lead to symmetry transformations. We show the importance of these special "trivial" transformations for the interconnection theorems which relate the symmetries of a system with its dynamics. We prove these theorems for general Hamiltonian systems. We apply the developed formalism to concrete physically relevant systems, in particular those which are diffeomorphism-invariant. The connection between the parameters of the symmetry transformations in the Hamiltonian and Lagrangian formalisms is found. The possible applications of our results are discussed.

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