Related papers: Dynamics and non-integrability of the double sprin…
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward…
This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish…
A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant…
The objective of the research is to develop a general method of constructing Lyapunov functions for non-linear non-autonomous differential inclusions described by ordinary differential equations with parameters. The goal has been attained…
Many experimental techniques aim at determining the Hamiltonian of a given system. The Hamiltonian describes the system's evolution in the absence of dissipation, and is often central to control or interpret an experiment. Here, we…
Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves - a seminal framework for studying the unstable growth of finite…
We propose a hybrid formulation of the linear inverted pendulum model for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings. Using a concept…
We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid…
The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
Evolutionary motions in a bouncing ball system consisting of a ball having a free fall in the Earth's gravitational field have been studied systematically. Because of nonlinear form of the equations of motion, evolutions show chaos for…
We investigate the dynamics of finite degree-of-freedom, planar mechanical systems with multiple sliding, unilateral frictional point contacts. A complete classification of systems with 2 sliding contacts is given. The contact-mode based…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
We study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrability conditions ensure the compatibility of this system and,…
We study numerically classical 1-dimensional Hamiltonian lattices involving inter-particle long range interactions that decay with distance like 1/r^alpha, for alpha>=0. We demonstrate that although such systems are generally characterized…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
The tangent dynamics of the Lyapunov modes and their dynamics as generated numerically - {\it the numerical dynamics} - is considered. We present a new phenomenological description of the numerical dynamical structure that accurately…