A geometric criterion for the existence of chaotic trajectories of a Hamiltonian system with two degrees of freedom and the configuration space a torus is given. As an application, positive topological entropy is established for a double pendulum problem.
We consider the classical and quantum dynamics of D0 branes within the Yang-Mills approximation. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed.
We study the vibration of lumped parameter systems whose constituents are described through novel constitutive relations, namely implicit relations between the forces acting on the system and appropriate kinematical variables such as the displacement and velocity of the constituent. In the classical approach constitutive expressions are provided for the force in terms of appropriate kinematical variables, which when substituted into the balance of linear momentum leads to a single governing ordinary...
Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.