Applying inversion to construct rational spiral curves

A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including those, assuming inflection.Comment: 18 pages, 11 figure

Fairing arc spline and designing by using cubic bézier spiral segments

This paper considers how to smooth three kinds of G 1 biarc models, the C-, S-, and J-shaped transitions, by replacing their parts with spiral segments using a single cubic Bézier curve. Arc spline is smoothed to G 2continuity. Use of a single curve rather than two has the benefit because designers and implementers have fewer entities to be concerned. Arc spline is planar, tangent continuous, piecewise curves made of circular arcs and straight line segments. It is important in manufacturing industries because of its use in the cutting paths for numerically controlled cutting machinery. Main contribution of this paper is to minimize the number of curvature extrema in cubic transition curves for further use in industrial applications such as non-holonomic robot path planning, highways or railways, and spur gear tooth designing

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version

Low Thrust Trajectories in Multi Body Regimes

More and more stringent and unique mission requirements motivate to exploring solutions, already in the preliminary mission analysis phase, going far beyond the classical chemical-Keplerian approach. The present dissertation deals with the analysis and the design of highly non linear orbits arising both from the inclusion of different gravitational sources in the dynamical models, and from the use of electric system for primary propulsion purposes. The equilibrium of different gravitational fields, on one hand, permits unique transfer solutions and operational orbits, on the other hand, the high thrust efficiency, characteristic of an electric device, reduces the propellant mass required to accomplish the transfer. Each of these models, and even better their combination, enables trajectories able to satisfy mission requirements not otherwise met, first of all to reduce the propellant mass fraction of a given mission. The inclusion of trajectory arcs powered by an electric thruster, providing a low thrust for extended duration, makes essential the use of optimal control theory in order to govern the thrust law and thus design the required transfers so as to minimizing/maximizing specific indexes. The goal is, firstly, to review the possible advantages and the main limits of dynamical models and, afterward, to define methodologies to preliminary design non-Keplerian missions both in interplanetary contexts and in the Earth-Moon system. Special emphasis is given to the study of dynamical systems through which the main features of the Circular Restricted Three Body Model (the first one among the non-Keplerian models) can be identified, implemented and used. Purely ballistic solutions enabled by this model are first independently explored and after considered as target orbits for electric thrusting phases. Electric powered arcs are used to link ballistic phases arising from the balancing of different gravitational influences. This concept is applied both for the exploration of planetary regions and for interplanetary transfer purposes. Together with low thrust missions to selenocentric orbits designed taking into account both the Earth and the Moon gravity, also transfer solutions toward periodic orbits moving in the Earth-Moon region are presented. These are designed considering electric thrusting arcs and ballistic segments exploring for free specific space regions. In brief, theoretical models deriving from dynamical system theory and from optimal control theory are employed to design non conventional orbits in non linear astrodynamics models