181 citations · 480 across the 7 of their papers we have counts for
7 papers
Stability boundary approximation of periodic dynamics
Anton O. Belyakov, Alexander P. Seyranian
We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linea…
Homoclinic, Subharmonic and Superharmonic Bifurcations for a Pendulum with Periodically Varying Length
Anton O. Belyakov, Alexander P. Seyranian
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the simplest model of child's swing. Melnikov's anal…
How to twirl a hula-hoop
Alexander P. Seyranian, Anton O. Belyakov
We consider twirling of a hula-hoop when the waist of a sportsman moves along an elliptic trajectory close to a circle. For the case of the circular trajectory, two families of exa…
On Nonlinear Dynamics of the Pendulum with Periodically Varying Length
Anton O. Belyakov, Alexander P. Seyranian
Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which…
Geometric phase around exceptional points
A. A. Mailybaev, O. N. Kirillov, A. P. Seyranian
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multid…
Unfolding of eigenvalue surfaces near a diabolic point due to a complex perturbation
O. N. Kirillov, A. A. Mailybaev, A. P. Seyranian
The paper presents a new theory of unfolding of eigenvalue surfaces of real symmetric and Hermitian matrices due to an arbitrary complex perturbation near a diabolic point. General…