Some Classes of Integrable Problems in Spatial Dynamics of a Rigid Body in a Nonconservative Force Field

2015 ◽  
Vol 210 (3) ◽  
pp. 292-330
Author(s):  
M. V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Field ◽  
Spatial Dynamics ◽  
Nonconservative Force

VARIETY OF THE CASES OF INTEGRABILITY IN DYNAMICS OF A SYMMETRIC 2D-, 3D- AND 4D-RIGID BODY IN A NONCONSERVATIVE FIELD

2013 ◽  
Vol 13 (07) ◽  
pp. 1340011 ◽  
Author(s):  
MAXIM V. SHAMOLIN
Keyword(s):  
Rigid Body ◽  
Force Field ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
General System ◽  
Rigid Bodies ◽  
Body Motion ◽  
Dynamical Equations ◽  
Vast Number ◽  
Nonconservative Force

A vast number of papers are devoted to studying the complete integrability of equations of four-dimensional rigid-body motion. Although in studying low-dimensional equations of motion of quite concrete (two- and three-dimensional) rigid bodies in a nonconservative force field, the author arrived at the idea of generalizing the equations to the case of a four-dimensional rigid body in an analogous nonconservative force field. As a result of such a generalization, the author obtained the variety of cases of integrability in the problem of body motion in a resisting medium that fills the four-dimensional space in the presence of a certain tracing force that allows one to reduce the order of the general system of dynamical equations of motion in a methodical way.

scholarly journals Cases of integrability corresponding to the pendulummotion on the plane

2017 ◽  
Vol 21 (10) ◽  
pp. 91-113
Author(s):  
M.V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Field ◽  
Invariant Form ◽  
Motion Equations ◽  
Plane Parallel ◽  
Free Rigid Body ◽  
Parallel Motion ◽  
Tracking Force ◽  
Similar Force

In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconserva- tive force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

scholarly journals Iso-energetic manifolds and motion possibility regions of rigid body in double force field

2005 ◽  
pp. 23-31
Author(s):  
D. B. Zotev ◽  
◽  
M. P. Kharlamov ◽  
Keyword(s):  
Rigid Body ◽  
Force Field
Sign in / Sign up

Export Citation Format

Share Document