Minimum time and minimum energy point-to-point trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an eecient way by a combination of a direct collocation and an indirect multiple shooting method. This combination links the beneets of both approa...

This paper is concerned with the efficient computation of periodic orbits in large-scale dynamical systems that arise after spatial discretization of partial differential equations (PDEs). A hybrid Newton–Picard scheme based on the shooting method is derived, which in its simplest form is the recursive projection method (RPM) of Shroff and Keller [SIAM J. Numer. Anal., 30 (1993), pp. 1099–1120]...

A class of singularly perturbed two-point boundary-value problems for second-order ordinary differential equations arising in chemical reactor theory is considered. In order to solve them numerically, a method is suggested in which the given interval (the domain of the definition of the differential equation) is divided into two subintervals called inner and outer regions. In the inner region a...

The study in this paper is a numerical integration of second-order three-point boundary value problems under two imposed nonlocal boundary conditions at t t0, t ξ, and t t1 in a general setting, where t0 < ξ < t1. We construct a two-stage Lie-group shooting method for finding unknown initial conditions, which are obtained through an iterative solution of derived algebraic equations in terms of ...

An analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperaturedependent viscosity and thermal radiation on an unsteady MHD free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate by taking into account the viscous dissipation effects. The g...

The ray shooting problem arises in many different contexts and is a bottleneck of ray tracing in computer graphics. Unfortunately, theoretical solutions to the problem are not very practical, while practical methods offer few provable guarantees on performance. Attempting to combine practicality with theoretical soundness, we show how to provably measure the average performance of any ray-shoot...

In the present study, field goal shooting skills of female basketball players were assessed in the background to their reasoning ability. The sample consists of 100 female intercollegiate basketball players (age = 21.05±1.67 yrs.). Shooting skills and reasoning ability were assessed by Johnson’s “Basketball Field Goal Speed Shooting Test” and Mixed Type Group Test of Intelligence prepared by Me...