For Hamiltonian systems of the form H= T(p) + V(q) a method is shown to construct explicit and time reversible symplectic integrators of higher order. For any even order there exists at least one symplectic integrator with exact coefficients. The simplest one is the 4th order integrator which agrees with one found by Forest and by Ned. For 6th and 8th orders, symplectic integrators with fewer s...

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

We consider three steps numerical integrator which is derived by collocation and interpolation of power series approximation solution to generate a linear multistep method which serves as the corrector. The corrector is then implemented in block method. We then propose another numerical integrator which is implemented in block method to serve as a constant order predictor to the corrector. Basi...

We derive an explicit second order reversible Poisson integrator for symmetric rigid bodies in space (i.e. without a fixed point). The integrator is obtained by applying a splitting method to the Hamiltonian after reduction by the S1 body symmetry. In the particular case of a magnetic top in an axisymmetric magnetic field (i.e. the Levitron) this integrator preserves the two momentum integrals....

In this paper, we present a variational integrator that is based on an approximation of the Euler–Lagrange boundary-value problem via Taylor’s method. This can be viewed as a special case of the shooting-based variational integrator. The Taylor variational integrator exploits the structure of the Taylor method, which results in a shooting method that is one order higher compared to other shooti...

This paper describes novel transconductor and an integrator circuits which can be used in integrated video frequency filters in bipolar technology. The transconductor consists of a parallel connection of a passive nominal transconductance and an active variable transconductance, resulting in good high frequency performance up to 70 MHz and less than 1% linearity error for input signals up to 2V...

The subject of controlling an integrator via a communication network nds many applications in modern control systems such as ATM network VBR control, load balancing in computer networks, etc. Stability conditions in closed form are derived for the arising feedback system, which consists of multiple controllers, an integrator and time-variant links between integrator and controllers. It will be ...

In this paper a very low-noise low-power correlated double sampled integrator has been presented. For attenuating the sampling thermal noise, two large capacitors are well incorporated in the integrator with no using large sampling and integrating capacitors that are necessary in ordinary integrators. The integrator is used in the front-end of a 24 bit, forth-order single-loop single-bit Delta-...

(Dated: June 16, 2001) We derive second and higher order explicit symplectic integrators for the charged particle motion in an s-dependent magnetic field with the paraxial approximation. The Hamiltonian of such a system takes the form of H = P k(pk − ak(~q, s)) + V (~q, s). This work solves a long-standing problem for modeling s-dependent magnetic elements. Important applications of this work i...