Abstract. If {an}n=1 and {bn}n=1 are two sequences such that a1 = b1 and bn + a1bn−1 + · · ·+ an−1b1 = nan (n > 1), then we say that (an, bn) is a Newton-Euler pair. In the paper we establish many formulas for Newton-Euler pairs, and then make use of them to obtain new results concerning some special sequences such as p(n), σ(n) and Bn, where p(n) is the number of partitions of n, σ(n) is the s...

The development of an algorithm to achieve optimal cyclic gaits in space for a thirteen-link biped and twelve actuated joints is proposed. The cyclic walking gait is composed of successive single support phases and impulsive impacts with full contact between the sole of the feet and the ground. The evolution of the joints are chosen as spline functions. The parameters to define the spline funct...

in this research optimal reconfiguration strategy of the improved srr reconfigurable mobile robot based on force-angle stability measure has been designed using genetic algorithm. path tracking nonlinear controller which keeps robot’s maximum stability has been designed and simulated in matlab. motion equations of the robot have been derived in parametric form by means of newton- euler, lagrang...

in this paper, a nonlinear model of the underactuated six degrees of freedom (6 dof) quadrotor helicopter was derived based on the newton-euler formalism. a new nonlinear robust control strategy was proposed to solve the stabilizing and path following problems in presence of external disturbances and parametric uncertainties. the proposed control structure consist of a sliding mode control base...

This paper gives a common theoretical treatment for gradient and Newton type methods for general classes of problems. First, for Euler-Lagrange equations Newton’s method is characterized as an (asymptotically) optimal variable steepest descent method. Second, Sobolev gradient type minimization is developed for general problems using a continuous Newton method which takes into account a ‘boundar...

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK are not commonly used in practice with large-scale numerical PDEs because of the difficulty solving stage equations. This paper introduces a theoretical algorithmic framework for nonlinear equations that arise from (and discontinuous Galerkin discretiza...

Using the Hodge decomposition on bounded domains the compressible Euler equations of gas dynamics are reformulated using a density weighted vorticity and dilatation as primary variables, together with the entropy and density. This formulation is an extension to compressible flows of the well-known vorticity-stream function formulation of the incompressible Euler equations. The Hamiltonian and a...

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid links, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system at hand are written. Then, using the DeNOC matrices associated with the velocity constraints of...