Classical Lagrangian and Hamiltonian Dynamics

2017 ◽  
pp. 89-129
Author(s):  
Taeyoung Lee ◽  
Melvin Leok ◽  
N. Harris McClamroch
Keyword(s):  
Hamiltonian Dynamics ◽  
Classical Lagrangian

scholarly journals Forecasting Hamiltonian dynamics without canonical coordinates

2021 ◽  
Author(s):  
Anshul Choudhary ◽  
John F. Lindner ◽  
Elliott G. Holliday ◽  
Scott T. Miller ◽  
Sudeshna Sinha ◽  
...  
Keyword(s):  
Hamiltonian Dynamics ◽  
Canonical Coordinates

scholarly journals On squaring the primary constraints in a generalized Hamiltonian dynamics

1994 ◽  
Vol 327 (1-2) ◽  
pp. 50-55 ◽  
Author(s):  
V.V. Nesterenko
Keyword(s):  
Hamiltonian Dynamics

Hamiltonian Chaos in a Model Alveolus

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
F. S. Henry ◽  
F. E. Laine-Pearson ◽  
A. Tsuda
Keyword(s):  
Reynolds Number ◽  
Fixed Point ◽  
Lyapunov Exponent ◽  
Fine Particles ◽  
Hamiltonian Dynamics ◽  
Maximal Lyapunov Exponent ◽  
Poincaré Sections ◽  
Pulmonary Acinus ◽  
Hamiltonian Chaos ◽  
Poincare Sections

In the pulmonary acinus, the airflow Reynolds number is usually much less than unity and hence the flow might be expected to be reversible. However, this does not appear to be the case as a significant portion of the fine particles that reach the acinus remains there after exhalation. We believe that this irreversibility is at large a result of chaotic mixing in the alveoli of the acinar airways. To test this hypothesis, we solved numerically the equations for incompressible, pulsatile, flow in a rigid alveolated duct and tracked numerous fluid particles over many breathing cycles. The resulting Poincaré sections exhibit chains of islands on which particles travel. In the region between these chains of islands, some particles move chaotically. The presence of chaos is supported by the results of an estimate of the maximal Lyapunov exponent. It is shown that the streamfunction equation for this flow may be written in the form of a Hamiltonian system and that an expansion of this equation captures all the essential features of the Poincaré sections. Elements of Kolmogorov–Arnol’d–Moser theory, the Poincaré–Birkhoff fixed-point theorem, and associated Hamiltonian dynamics theory are then employed to confirm the existence of chaos in the flow in a rigid alveolated duct.

Hamiltonian dynamics of Poincaré gauge theory: General structure in the time gauge

1983 ◽  
Vol 28 (10) ◽  
pp. 2455-2463 ◽  
Author(s):  
M. Blagojević ◽  
I. A. Nikolić
Keyword(s):  
Gauge Theory ◽  
Hamiltonian Dynamics ◽  
General Structure

scholarly journals Hamiltonian Dynamics of Polygons and Integrability

1997 ◽  
Vol 205 (1) ◽  
pp. 133-147
Author(s):  
Michael L Frankel
Keyword(s):  
Hamiltonian Dynamics
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