A Hamiltonian theory for an elastic earth: Canonical variables and kinetic energy

1990 ◽  
Vol 49 (3) ◽  
pp. 303-326 ◽  
Author(s):  
Juan Getino ◽  
Jose M. Ferr�ndiz
Keyword(s):  
Kinetic Energy ◽  
Elastic Earth ◽  
Canonical Variables ◽  
Hamiltonian Theory

A Hamiltonian theory for an elastic earth: Elastic energy of deformation

1991 ◽  
Vol 51 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Juan Getino ◽  
José M. Ferrándiz
Keyword(s):  
Elastic Energy ◽  
Elastic Earth ◽  
Hamiltonian Theory

Hamiltonian theory of the generalized oscillation-centre transformation

1988 ◽  
Vol 39 (1) ◽  
pp. 81-102 ◽  
Author(s):  
B. Weyssow ◽  
R. Balescu
Keyword(s):  
High Frequency ◽  
Ponderomotive Force ◽  
Hamiltonian Formalism ◽  
Larmor Frequency ◽  
Static Field ◽  
Canonical Variables ◽  
Hamiltonian Theory ◽  
External Frequency ◽  
High Frequency Electromagnetic Field ◽  
Physical Quantities

The theory of the slow reaction of a charged particle in the combined presence of a strong quasi-static magnetic field and a high-frequency electromagnetic field (generalized oscillation-centre motion) is constructed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The theory combines the features studied in our previous works for the case in which only one of the previously mentioned fields is present. The new averaging transformation is based on the fact that the Larmor frequency of the quasi-static field is of the same order as the external frequency of the high-frequency field. Our theory is manifestly gauge-invariant and involves only physical quantities (particle velocity and electromagnetic fields). Explicit expressions for the drift velocity of the oscillation centre and for the ponderomotive force are derived.

A Hamiltonian theory for an elastic earth: Secular rotational acceleration

1991 ◽  
Vol 52 (4) ◽  
pp. 381-396 ◽  
Author(s):  
Juan Getino ◽  
Jos� M. Ferr�ndiz
Keyword(s):  
Rotational Acceleration ◽  
Elastic Earth ◽  
Hamiltonian Theory

A manifestly gauge-invariant Hamiltonian theory of the oscillation-centre dynamics

1987 ◽  
Vol 37 (3) ◽  
pp. 467-486 ◽  
Author(s):  
B. Weyssow ◽  
R. Balescu
Keyword(s):  
High Frequency ◽  
Ponderomotive Force ◽  
Hamiltonian Formalism ◽  
Gauge Invariant ◽  
Canonical Variables ◽  
Hamiltonian Theory ◽  
Special Cases ◽  
High Frequency Electromagnetic Field ◽  
Particle Velocities ◽  
Field Oscillation

The theory of the slow reaction of charged particles in the presence of a high-frequency electromagnetic field (oscillation-centre motion) is developed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The flexibility introduced by the latter features allows us to construct a theory which is manifestly gauge-invariant and involves only physical concepts (electromagnetic fields and particle velocities instead of potentials and canonical momenta). A complete description of the oscillation-centre dynamics is derived. The known expressions of the ponderomotive force are derived as special cases of our theory.

scholarly journals A note on the Hamiltonian theory of quantization

1945 ◽  
Vol 183 (994) ◽  
pp. 316-328 ◽  
Keyword(s):  
Proper Choice ◽  
Maxwell Field ◽  
Supplementary Condition ◽  
Canonical Forms ◽  
Field Equations ◽  
Standard Methods ◽  
Canonical Variables ◽  
Hamiltonian Theory ◽  
In The Beginning

In this note a study is made of the field equations which are obtained from varying a Lagrangian subject to auxiliary conditions. It is shown that with proper choice of conjugate variables and the Hamiltonian, they can be brought to canonical forms and thus permit quantization in the usual way. It is then pointed out that for fields with some conjugate variables missing, it is sometimes possible to introduce such auxiliary conditions without affecting the field equations but with the result that all the new canonical variables are present, thus allowing the application of the standard methods of quantization. To illustrate this, the Maxwell field is quantized subject to ∇ . A + c -1 ∂ ɸ /∂ t = 0. The usual supplementary condition on ψ , (∇ . A + c -1 ∂ ɸ /∂ t ) ψ = 0, is found to be shifted to other conditions on ψ . Though in the beginning there are apparently some complications, the final result is simple.

Dependence of the joint configuration on the dynamic immobility fulcrum

2019 ◽  
pp. 108-114
Author(s):  
A. D. Kozlov ◽  
Yu. P. Potekhina
Keyword(s):  
Kinetic Energy ◽  
Convex Surface ◽  
The Other ◽  
Concave Surface ◽  
Joint Configuration ◽  
Articular Surfaces

Although joints with synovial cavities and articular surfaces are very variable, they all have one common peculiarity. In most cases, one of the articular surfaces is concave, whereas the other one is convex. During the formation of a joint, the epiphysis, which has less kinetic energy during the movements in the joint, forms a convex surface, whereas large kinetic energy forms the epiphysis with a concave surface. Basing on this concept, the analysis of the structure of the joints, allows to determine forces involved into their formation, and to identify the general patterns of the formation of the skeleton.

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