Analytical perturbative theories of motion in highly inhomogeneous gravitational fields : Ariadna AO/1-6790/11/NL/CBI

In this report we show that modern computer performances and state-of-the-art algebraic manipulator software are sufficiently developed to carry out our generalised analytical perturbative theory. This report addresses three technical aspects to develop a general perturbative theory and illustrates its power by applying it to investigate the inhomogeneous gravitational fields of asteroids

Uses Made of Computer Algebra in Physics

Computer algebra is a tool building activity. This paper is a review of acceptance of this tool by physicists and theoretical chemists during the period from the EUROSAM-79 survey to the Spring of 1988, as reflected by the literature which quotes computer algebra. After considering the traditional areas of application; celestial mechanics, relativity and quantum mechanics, we extend our examination to other areas of physics which would appear, from the literature, to be using computer algebra efficiently: fluid mechanics, plasma physics, optics, perturbation technology, continuum mechanics, numerical analysis for physics, mechanics, non-linear evolution equations, theoretical chemistry and other applications

On the History of Computer Algebra at the Keldysh Institute of Applied Mathematics

Abstract: The authors consider the history of Computer Algebra (CA) developmen

Launch window analysis of satellites in high eccentricity or large circular orbits

Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions

The Main Problem in Satellite Theory Revisited

Abstract. Using the elimination of the parallax followed by the Delaunay normalization, we present a procedure for calculating a normal form of the main problem (J2 perturbation only) in satellite theory. This procedure is outlined in such a way that an object-oriented automatic symbolic manipulator based on a hierarchy of algebras can perform this computation. The Hamiltonian after the Delaunay normalization is presented to order six explicitly in closed form, that is, in which there is no expansion in the eccentricity. The corresponding generating function and transformation of coordinates, too lengthy to present here to the same order; the generator is given through order four

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented

What is Robotics: Why Do We Need It and How Can We Get It?

Robotics is an emerging synthetic science concerned with programming work. Robot technologies are quickly advancing beyond the insights of the existing science. More secure intellectual foundations will be required to achieve better, more reliable and safer capabilities as their penetration into society deepens. Presently missing foundations include the identification of fundamental physical limits, the development of new dynamical systems theory and the invention of physically grounded programming languages. The new discipline needs a departmental home in the universities which it can justify both intellectually and by its capacity to attract new diverse populations inspired by the age old human fascination with robots. For more information: Kod*la