The Theory of Adiabatic Invariants

1999 ◽  
pp. 179-233 ◽  
Author(s):  
Dino Boccaletti ◽  
Giuseppe Pucacco
Keyword(s):  
Adiabatic Invariants

Generalized adiabatic invariants in classical mechanics

1968 ◽  
Vol 1 (3) ◽  
pp. 326-330
Author(s):  
L Navarro ◽  
L M Garrido
Keyword(s):  
Classical Mechanics ◽  
Adiabatic Invariants

scholarly journals Adiabatic invariants drive rhythmic human motion in variable gravity

2019 ◽  
Author(s):  
N. Boulanger ◽  
F. Buisseret ◽  
V. Dehouck ◽  
F. Dierick ◽  
O. White
Keyword(s):  
Motor Control ◽  
Human Motion ◽  
Adiabatic Invariants ◽  
Human Motor Control ◽  
Changing Environments ◽  
Human Movements ◽  
Human Motor ◽  
Variable Gravity ◽  
Points Of View ◽  
Motor Strategies

AbstractNatural human movements are stereotyped. They minimise cost functions that include energy, a natural candidate from mechanical and physiological points of view. In time-changing environments, however, motor strategies are modified since energy is no longer conserved. Adiabatic invariants are relevant observables in such cases, although they have not been investigated in human motor control so far. We fill this gap and show that the theory of adiabatic invariants explains how humans move when gravity varies.

scholarly journals Borel summation of adiabatic invariants

Nonlinearity ◽  
2004 ◽  
Vol 17 (4) ◽  
pp. 1509-1519 ◽  
Author(s):  
O Costin ◽  
L Dupaigne ◽  
M D Kruskal
Keyword(s):  
Adiabatic Invariants ◽  
Borel Summation

scholarly journals Exact solution of the planar motion of three arbitrary point vortices

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1530017
Author(s):  
Robert Conte ◽  
Laurent de Seze
Keyword(s):  
Exact Solution ◽  
Equilibrium Configuration ◽  
Relative Equilibrium ◽  
Arbitrary Point ◽  
Triple Collision ◽  
Stability Conditions ◽  
Adiabatic Invariants ◽  
The Third ◽  
Elastic Diffusion ◽  
Equilateral Triangles

We give an exact quantitative solution for the motion of three vortices of any strength, which Poincaré showed to be integrable. The absolute motion of one vortex is generally biperiodic: in uniformly rotating axes, the motion is periodic. There are two kinds of relative equilibrium configuration: two equilateral triangles and one or three colinear configurations, their stability conditions split the strengths space into three domains in which the sets of trajectories are topologically distinct. According to the values of the strengths and the initial positions, all the possible motions are classified. Two sets of strengths lead to generic motions other than biperiodic. First, when the angular momentum vanishes, besides the biperiodic regime there exists an expansion spiral motion and even a triple collision in a finite time, but the latter motion is nongeneric. Second, when two strengths are opposite, the system also exhibits the elastic diffusion of a vortex doublet by the third vortex. For given values of the invariants, the volume of the phase space of this Hamiltonian system is proportional to the period of the reduced motion, a well known result of the theory of adiabatic invariants. We then formally examine the behaviour of the quantities that Onsager defined only for a large number of interacting vortices.

On the conservation of adiabatic invariants for a system of coupled rotators

1997 ◽  
Vol 104 (3-4) ◽  
pp. 253-268 ◽  
Author(s):  
G. Benettin ◽  
A. Carati ◽  
F. Fassò
Keyword(s):  
Adiabatic Invariants ◽  
Coupled Rotators

On the adiabatic invariants

Enrico Fermi ◽  
2004 ◽  
pp. 85-114
Author(s):  
Tullio Levi-Civita
Keyword(s):  
Adiabatic Invariants
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