scholarly journals Helicity and spin conservation in linearized gravity

2021 ◽  
Vol 53 (11) ◽  
Author(s):  
Sajad Aghapour ◽  
Lars Andersson ◽  
Reebhu Bhattacharyya
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Spin Part ◽  
Linearized Gravity ◽  
Conservation Property

AbstractThe duality-symmetric, Maxwell-like, formulation of linearized gravity introduced by Barnett (New J Phys 16, 2014) is used to generalize the conservation laws for helicity, the spin part of angular momentum, and spin-flux, to the case of linearized gravity. These conservation laws have been shown to follow from the conservation property of the helicity array, an analog of Lipkin’s zilch tensor. The analog of the helicity array for linearized gravity is constructed and is shown to be conserved.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

Non-axisymmetric Unstable Modes in a Thin Differentially Rotating Gaseous Disk

1991 ◽  
Vol 02 (01) ◽  
pp. 367-370
Author(s):  
M.H.M. HEEMSKERK ◽  
G.J. SAVONIJE
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Numerical Solutions ◽  
Gravitational Attraction ◽  
Rotating Disc ◽  
Central Mass ◽  
Reflecting Boundaries ◽  
Self Gravity ◽  
Axisymmetric Perturbations ◽  
Gaseous Disc

We consider the linear stability of a thin differentially rotating gaseous disc with reflecting boundaries against non-axisymmetric perturbations. We assume the unperturbed disc to be in centrifugal equilibrium with the gravitational attraction of a central mass M, and consider discs whose mass can be neglected relative to M. We discuss the relevant conservation laws for the energy and angular momentum of linear non-axisymmetric modes in a thin rotating disc without self-gravity and illustrate the basic mode amplification mechanisms with help of some of our numerical solutions [1].

Proof of the no-interaction theorem without hamiltonian and lagrangian formalism

1994 ◽  
Vol 445 (1923) ◽  
pp. 221-229 ◽  
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Lagrangian Formalism ◽  
The Individual ◽  
Individual Particles

The proofs of the no-interaction theorem have been given by many authors in the framework of hamiltonian and lagrangian formalism. They are based on the assumption that there is hamiltonian or lagrangian describing the interaction between particles. This paper presents the proof without such an assumption for one, two, three and four particles. We assume the conservation laws for the linear and angular momentum that are the sums of the respective quantities of individual particles. Then there is no interaction, i. e. the worldlines of the individual particles are straight.

Variational principles of guiding centre motion

1983 ◽  
Vol 29 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Robert G. Littlejohn
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Conservation Laws ◽  
Variational Principles ◽  
Equations Of Motion ◽  
Phase Volume ◽  
Rigorous Derivation ◽  
Volume Energy ◽  
Symmetric Systems

An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.

scholarly journals HIGHER-ORDER GEOMETRIC INTEGRATORS FOR A CLASS OF HAMILTONIAN SYSTEMS

2013 ◽  
Vol 11 (01) ◽  
pp. 1450009 ◽  
Author(s):  
ASIF MUSHTAQ ◽  
ANNE KVÆRNØ ◽  
KÅRE OLAUSSEN
Keyword(s):  
Angular Momentum ◽  
Differential Equations ◽  
Conservation Laws ◽  
Large Class ◽  
Hamiltonian Systems ◽  
Symplectic Geometry ◽  
Hamiltonian Mechanics ◽  
Rotation Invariant ◽  
Geometric Integrators ◽  
Kinetic And Potential Energies

We discuss systematic extensions of the standard (Störmer–Verlet) method for integrating the differential equations of Hamiltonian mechanics. Our extensions preserve the symplectic geometry exactly, as well as all Nöether conservation laws caused by joint symmetries of the kinetic and potential energies (like angular momentum in rotation invariant systems). These extensions increase the accuracy of the integrator, which for the Störmer–Verlet method is of order τ2 for a timestep of length τ, to higher-orders in τ. The schemes presented have, in contrast to most previous proposals, all intermediate timesteps real and positive. The schemes increase the relative accuracy to order τN (for N = 4, 6 and 8) for a large class of Hamiltonian systems.

Synthesis of a Compensated Kick Pattern for Humanoid Robots Using Conservation Laws

2006 ◽  
Author(s):  
Ali Meghdari ◽  
Seyed Hossein Tamaddoni ◽  
Farid Jafari
Keyword(s):  
Computer Simulation ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Humanoid Robot ◽  
Humanoid Robots ◽  
Ball Velocity ◽  
Energy Consuming ◽  
The Law

The motivation of this work is to synthesize a kicking pattern for a humanoid robot with consideration of various objectives such as retaining its balance even after the kick is done and reducing the undesired angular momentum using both hands and torso. This kick pattern is designed so that a desirable ball velocity is achieved. In this paper, the law of conservation of angular momentum is used to generate a less energy consuming trajectory. Effectiveness of the proposed method is verified using computer simulation and is tested on Sharif CEDRA humanoid robot.

scholarly journals Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams

2012 ◽  
Vol 20 (4) ◽  
pp. 3563 ◽  
Author(s):  
O. V. Angelsky ◽  
A. Ya. Bekshaev ◽  
P. P. Maksimyak ◽  
A. P. Maksimyak ◽  
S. G. Hanson ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Internal Energy ◽  
Orbital Angular Momentum ◽  
Energy Flow ◽  
Mechanical Action ◽  
Spin Part ◽  
Orbital Rotation ◽  
Light Beams

On the probability of artificial nuclear transformations and its connection with the vector model of the nucleus

1934 ◽  
Vol 30 (4) ◽  
pp. 561-566 ◽  
Author(s):  
M. Goldhaber
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Nuclear Reaction ◽  
Nuclear Spin ◽  
Experimental Result ◽  
Vector Model ◽  
Spin Part ◽  
Interaction Forces ◽  
Constant Of Motion ◽  
Total Interaction

1. The theorem of quantum mechanics that “the spin part of the angular momentum is approximately a constant of motion provided that the forces depending on the direction of the spins are small compared with the total interaction forces” is introduced into the discussion of artificial nuclear transformations. A definition is given for the terms “probable” and “not probable” nuclear reaction.2. Attention is drawn to the experimental result that the reaction Li6 + H1 → He4 + He3 is more probable than the reaction Li7 + H1 → 2He4, and an explanation is suggested.3. The nuclear spin of Lie is derived from nuclear transformations and found to be 1.4. Similar derivations for the spins of H3, He3 and B11 are summarised in a table.

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