Holonomic and Pfaffian nonholonomic systems are dynamical systems whose generalized coordinates and velocities are subject to smooth constraints. These systems are usually described by second order differential equations of motion and algebraic equations of constraint. We present an optimal control formulation for these systems that utilizes the multiplier rule to append both the equations of m...

The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of wave equations are formulated as continuous non-autonomous dynamical systems (cocycles). A sufficient and necessary condition for the existence of pullback attractors is established. The required compactness for the existence of pullback attr...

We show here the separability of Hamilton-Jacobi equation for a hierarchy of integrable Hamiltonian systems obtained from the constrained flows of the Jaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian systems is constructed. The associated r-matrices depend not only on the spectral parameters, but also on the dynamical variables and, for consistency, have to obey t...

Abstract. The system of weak normality equations constitutes a part in the complete system of normality equations. Solutions of each of these two systems of equations are associated with some definite classes of Newtonian dynamical systems in Riemannian manifolds. In this paper for the case of simplest flat Riemannian manifold M = R with n> 3 we show that there exist solutions of weak normality...

In this paper, we generalize the so-called “nudging” algorithm in order to identify the initial condition of a dynamical system from experimental observations. The standard nudging algorithm consists in adding to the state equations of a dynamical system a feedback term, which is proportional to the difference between the observation and its equivalent quantity computed by the resolution of the...

In this paper, a dynamical model-based SMC (Sliding Mode Control) is proposed fortrajectory tracking of a 3-RPS (Revolute, Prismatic, Spherical) parallel manipulator. With ignoring smallinertial effects of all legs and joints compared with those of the end-effector of 3-RPS, the dynamical model ofthe manipulator is developed based on Lagrange method. By removing the unknown Lagrange multipliers...