Local and global aspects of a generalized Hamiltonian theory

2005 ◽  
pp. 169-199
Author(s):  
Robert Cawley
Keyword(s):  
Hamiltonian Theory

ON THE THEORY OF THE DOPPLER EFFECT IN A MOVING MEDIUM

1998 ◽  
Vol 13 (01) ◽  
pp. 1-6 ◽  
Author(s):  
BRUNO BERTOTTI
Keyword(s):  
Solar Wind ◽  
Doppler Effect ◽  
Dispersive Medium ◽  
Time Derivative ◽  
Optical Path ◽  
Moving Medium ◽  
Perturbation Theorem ◽  
Hamiltonian Theory ◽  
The Doppler Effect ◽  
Definition Of

The increase in the accuracy of Doppler measurements in space requires a rigorous definition of the observed quantity when the propagation occurs in a moving, and possibly dispersive medium, like the solar wind. This is usually done in two divergent ways: in the phase viewpoint it is the time derivative of the correction to the optical path; in the ray viewpoint the signal is obtained form the deflection produced in the ray. They can be reconciled by using the time derivative of the optical path in the Lagrangian sense, i.e. differentiating from ray to ray. To rigorously derive this result an understanding, through relativistic Hamiltonian theory, of the delicate interplay between rays and phase is required; a general perturbation theorem which generalizes the concept of the Doppler effect as a Lagrangian derivative is proved. Relativistic retardation corrections O(v) are obtained, well within the expected sensitivity of Doppler experiments near solar conjunction.

scholarly journals A tunneling Hamiltonian theory of 0-π transition ind-wave superconductor/ferromagnetic-insulator heterostructures

2010 ◽  
Vol 248 ◽  
pp. 012039
Author(s):  
Shiro Kawabata ◽  
Satoshi Kashiwaya ◽  
Yukio Tanaka ◽  
Alexander A Golubov ◽  
Yasuhiro Asano
Keyword(s):  
Hamiltonian Theory

The Lagrangian-Hamiltonian Theory

1999 ◽  
pp. 121-186
Author(s):  
M. A. Trump ◽  
W. C. Schieve
Keyword(s):  
Hamiltonian Theory

Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents

1994 ◽  
Vol 261 ◽  
pp. 65-74 ◽  
Author(s):  
Jon Wright ◽  
Dennis B. Creamer
Keyword(s):  
Free Surface ◽  
Nonlinear Effects ◽  
Linear Representation ◽  
Finite Depth ◽  
Transformation Method ◽  
Leading Order ◽  
Short Waves ◽  
Hamiltonian Theory ◽  
Lie Transformation ◽  
Correct Implementation

We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived.

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