In this paper we consider the problem of constructing equations describing the states of dissipative dynamical systems (media with absorption or damping). The approaches of Lagrange and Hamilton are discussed. A non-symplectic extension of the Poisson brackets is formulated. The application of the Hamiltonian formalism here makes it possible to obtain explicit equations for the dynamics of a nonlinear elastic system with damping and a one-dimensional continuous medium with internal friction.

Topics
Thermodynamic systems, Laws of friction, Elasticity theory, Hamiltonian mechanics, Dynamical systems
1.
L.V.
 
Prokhorov
,
S.V.
 
Shabanov
,
Hamiltonian mechanics of calibration systems
(
St. Petersburg University Press
,
St. Petersburg
,
1997
).
Google Scholar
 
2.
A.A.
 
Isaev
,
M. Yu.
 
Kovalevsky
,
S.V.
 
Peletminsky
,
Theoretical and Mathematical Physics
.
108
(
2
),
263
–
296
(
1995
).
Google Scholar
 
3.
B.A.
 
Dubrovin
,
I.M.
 
Krichever
,
S.P.
 
Novikov
,
Encyclopedia of Mathematical Sciences
(
Springer, Berlin
,
Heidelberg, New York
,
1988
).
Google Scholar
 
4.
A.A.
 
Bogush
,
L.G.
 
Moroz
,
Introduction to the theory of classical fields
(
Publishing House of Science and Technology
,
Minsk
,
1968
).
Google Scholar
 
5.
L.V.
 
Prokhorov
,
Physics of Elementary Particles and the Atomic Nucleus
.
38
(
3
),
696
–
733
(
2007
).
Google Scholar
 
6.
V.B.
 
Ibarra-Sierra
,
A.
 
Inzaldo-Menessis
,
Annals of Physics
,
335
,
86
–
107
(
2013
).
https://doi.org/10.1016/j.aop.2013.04.013
Google Scholar
Crossref
Search ADS
 
This content is only available via PDF.
© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.