Noetherian Perspective of Eulerian Motion of a Free Rigid Body

1997 ◽  
Vol 20 (1) ◽  
pp. 193-196
Author(s):  
Yoshihiko Nakamura ◽  
Ranjan Mukherjee
Keyword(s):  
Rigid Body ◽  
Free Rigid Body

LIE–TROTTER FORMULA AND POISSON DYNAMICS

1999 ◽  
Vol 09 (03) ◽  
pp. 555-559 ◽  
Author(s):  
MIRCEA PUTA
Keyword(s):  
Rigid Body ◽  
Euler Equations ◽  
Bloch Equations ◽  
Free Rigid Body ◽  
Trotter Formula ◽  
Maxwell Bloch Equations

We construct via the Lie–Trotter formula some explicit Poisson integrators for the Maxwell–Bloch equations from laser-matter dynamics, the Euler equations of the free rigid body and the equations of the rigid body with a spinning rotor.

Nonlinear Hall MHD and electrostatic ion–cyclotron stationary waves: a Hamiltonian-geometric viewpoint

2007 ◽  
Vol 73 (5) ◽  
pp. 687-700 ◽  
Author(s):  
J. F. McKENZIE ◽  
R. L. MACE ◽  
T. B. DOYLE
Keyword(s):  
Rigid Body ◽  
Periodic Solutions ◽  
Soliton Solutions ◽  
Stationary Waves ◽  
Dynamical Equations ◽  
Free Rigid Body ◽  
Ion Cyclotron ◽  
Hall Mhd

AbstractSome supplementary results and interpretations on the theory of Hall MHD solitons (McKenzie and Doyle 2002 Phys. Plasmas9, 55) are presented. It is shown that the Hall MHD soliton reduces, in the appropriate limit, to an electrostatic ion–cyclotron soliton. It is also shown how the dynamical equations governing the Hall MHD soliton can be obtained from a Hamiltonian H. Soliton solutions correspond to H = 0, periodic solutions to H < 0 and rotation-type solutions to H >0. Possible applications are discussed. A non-canonical Hamiltonian picture is developed and compared to the well-known example of a free rigid body.

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.

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