In this paper, the effect of normal impact on the mathematical modeling of flexible multiple links is investigated. The response of such a system can be fully determined by two distinct solution procedures. Highly nonlinear differential equations are exploited to model the falling phase of the system prior to normal impact; and algebraic equations are used to model the normal collision of this ...

In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is “transfer matrix method” which is based on the changes in the vibration modes at the vicinity of any discontinu...

Joel E. Cohen (1981) conjectured that any stochastic matrix P = fpi;jg could be represented by some circle rotation f in the following sense: For some partition fSig of the circle into sets consisting of …nite unions of arcs, we have (*) pi;j = (f (Si) \ Sj) = (Si), where denotes arc length. In this paper we show how cycle decomposition techniques originally used (Alpern, 1983) to establish Coh...

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying...

Ion optics with electrostatic lenses is presented using the standard matrix formalism of magnetic ion optics. We introduce the paraxial ray equation which is appropriate to systems with rotational symmetry. The first-order solutions of the paraxial ray equation are derived. The resulting transport matrices can be used to study systems with acceleration tube lenses, aperture lenses, einzel lense...