scholarly journals Guiding-center recursive Vlasov and Lie-transform methods in plasma physics

2009 ◽  
Vol 75 (5) ◽  
pp. 675-696 ◽  
Author(s):  
A. J. BRIZARD ◽  
A. MISHCHENKO
Keyword(s):  
Phase Space ◽  
Plasma Physics ◽  
Hamiltonian Dynamics ◽  
Transform Methods ◽  
Lie Transform ◽  
Recursive Solution ◽  
Space Transformation

AbstractThe gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work clarifies the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center recursive Vlasov method and the method of Lie-transform phase-space transformations.

scholarly journals Quantum gravity, dynamical phase-space and string theory

2014 ◽  
Vol 23 (12) ◽  
pp. 1442006 ◽  
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
String Theory ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Symplectic Geometry ◽  
Complex Geometry ◽  
Hamiltonian Dynamics ◽  
Natural Extension ◽  
Dynamical Phase

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).

Hamiltonian Dynamics and Phase Space

2019 ◽  
pp. 83-108
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Hamiltonian Dynamics ◽  
Orbital Dynamics ◽  
Legendre Transform ◽  
Lagrange Equations ◽  
Conservation Of Energy ◽  
Hamiltonian Equations ◽  
Generalized Coordinates ◽  
Conservation Of Momentum

Hamiltonian dynamics are derived from the Lagrange equations through the Legendre Transform that expresses the equations of dynamics in terms of the Hamiltonian, which is a function of the generalized coordinates and of their conjugate momenta. Consequences of the Lagrangian and Hamiltonian equations of dynamics are conservation of energy and conservation of momentum, with applications to collisions and orbital dynamics. Action-angle coordinates can be defined for integrable Hamiltonian systems and reduce all dynamical motions to phase space trajectories on a hyperdimensional torus.

Phase space geometry and stochasticity thresholds in Hamiltonian dynamics

2000 ◽  
Vol 62 (5) ◽  
pp. 6078-6081 ◽  
Author(s):  
Monica Cerruti-Sola ◽  
Marco Pettini ◽  
E. G. D. Cohen
Keyword(s):  
Phase Space ◽  
Hamiltonian Dynamics ◽  
Space Geometry ◽  
Phase Space Geometry

Beamline optimization and phase space transformation (abstract)a)

1995 ◽  
Vol 66 (2) ◽  
pp. 2064-2064
Author(s):  
J. Bahrdt ◽  
U. Flechsig ◽  
F. Senf
Keyword(s):  
Phase Space ◽  
Space Transformation

scholarly journals Dynamics and Control of Humanoid Robots: A Geometrical Approach

2010 ◽  
Vol 1 (4) ◽  
Author(s):  
Vladimir G. Ivancevic ◽  
Tijana T. Ivancevic
Keyword(s):  
Phase Space ◽  
Hamiltonian Dynamics ◽  
Fitness Function ◽  
Hamiltonian Formalism ◽  
Humanoid Robots ◽  
Geometrical Approach ◽  
Dynamics And Control ◽  
Definition Of ◽  
Configuration Manifold ◽  
And Control

AbstractThis paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the ‘covariant force law’, the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated ‘humanoid velocity phase space’, while autonomous Hamiltonian dynamics is formulated on the associated ‘humanoid momentum phase space’. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples.

Coarse-grained entropy decrease and phase-space focusing in Hamiltonian dynamics

2005 ◽  
Vol 72 (1) ◽  
Author(s):  
Arjendu K. Pattanayak ◽  
Daniel W. C. Brooks ◽  
Anton de la Fuente ◽  
Lawrence Uricchio ◽  
Edward Holby ◽  
...  
Keyword(s):  
Phase Space ◽  
Hamiltonian Dynamics ◽  
Coarse Grained

scholarly journals A Family of Hierarchical Symplectic Maps for N-body Simulations with Post-Newtonian Corrections

2017 ◽  
Vol 45 ◽  
pp. 1760021
Author(s):  
Guilherme Gonçalves Ferrari
Keyword(s):  
Phase Space ◽  
Body Problem ◽  
Hamiltonian Dynamics ◽  
Symplectic Maps ◽  
Time Step ◽  
Phase Space Volume ◽  
Time Stepping ◽  
Adaptive Time ◽  
The Individual ◽  
Space Volume

Symplectic maps are well known for preserving the phase-space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times, such as the [Formula: see text]-body problem. However, when combined with a varying time-step scheme, they end up losing its symplecticity and become numerically inefficient. We address this problem by using a recursive Hamiltonian splitting based on the time-symmetric value of the individual time-steps required by the particles in the system. We present a family of 48 quasi-symplectic maps with different orders of convergence (2nd-, 4th- & 6th-order) and three time-stepping schemes: i) 16 using constant time-steps, ii) 16 using shared adaptive time-steps, and iii) 16 using hierarchical (individual) time-steps. All maps include post-Newtonian corrections up to order 3.5PN. We describe the method and present some details of the implementation.

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