3rd ENOC ProceedingsIndex

Bushes of normal modes for nonlinear mechanical systems with discrete symmetry

G.M. Chechina, V.P. Sakhnenkoa, M.Yu. Zekhtsera, H.T. Stokesb, S. Carterb, and D.M. Hatchb

aDepartment of Physics, Rostov State University, Zorge 5, 344090 Rostov-on-don, Russia

bDepartment of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA


The normal modes in a linear mechanical system with discrete symmetry are independent of each other. When such systems are non-linear, these modes are all coupled to each other. However, if a single mode is excited, this excitation spreads to only a finite number of other modes. This collection of modes is called a ``bush of modes''. The dynamical behavior of a bush of modes depends on the form of its Hamiltonian. This allows us to put bushes into universality classes. As an example, we list the one, two, and three-dimensional bushes for all possible free molecules with crystallographic point-group symmetry. (Our analysis can be applied not only to molecules but to any macroscopic mechanical system with point symmetry as well.) We find 363 distinct bushes that belong to 11 different classes. We give the form of the Hamiltonian for each of those 11 classes.




Contact information

G.M. Chechin, V.P. Sakhnenko and M.Yu. Zekhtser

Department of Physics
Rostov State University
Zorge 5
344090 Rostov-on-don

e-mail: chechin@phys.rnd.runnet.ru

H.T. Stokes, S. Carter and D.M. Hatch

Department of Physics and Astronomy
Brigham Young University
Provo, Utah 84602

e-mail: stokesh@byu.edu

3rd ENOC ProceedingsIndex