OPAL(ID:8289/)

Matrix and celestial emchanics system based on the Prorab interpreter
References:
  • Kutuzov, A. L. "The OPAL programming system for analytical theories in celestial mechanics" Pis'ma v Astronomicheskii Zhurnal, 1, Jan. 1975, p. 43-46.) Soviet Astronomy Letters, vol. 1, Jan.-Feb. 1975, p. 21, 22 view details Abstract: Programming system in computer M-20 language has been constructed which permits to perform all basic operations with literal Poisson series. The proper choice of algorithms and the use of computer language permit a considerable economy in the computer fast memory and time as compared with programs in algorithmic languages. The system can be used to solve many problems of celestial mechanics. Extract: Introduction
    Introduction
    Celestial mechanics is today confronted with situations, such as spacecraft flights to other bodies of the solar in which the coordinates of celestial bodies must be established to very high precision, an accuracy that can be achieved only with modern computer technology.
    Numerical integration of the equations of motion has the that the calculations have to be repeated for each new system of input data. Another approach is to solve the differential equations in symbolic form. The coordinates can then be obtained simply by replacing  the syrnbols in the equations by their numerical values. This procedure significantly economizes time, but there is some difficulty in "teaching" the machine how to perform operations with symbolic expressions.
    Extract: Programming Principles
    Programming Principles
    Existing programming languages and systems designed for transforming analytic expressions on computers are too general in character to be well-suited for solving celestial-mechanics problems; they place excessive demands on the memory and computation time. One therefore needs special programming systems, comprising a set of subprograms for operations with Poisson series of the form where the ai and ßj are integers, the xi are metric variables, the yj are angular variables, and the q,,,, ßj are numerical coefficients. The solutions of most celestialmechanics problems reduce to operations with such series. We have attempted to develop such a programming system for the medium-capacity type M-20 computer.
    Maximum economy of memory and computer time has been achieved by using machine language and optimum operation algorithms, especially for the addition and multiplication of series. This system, which we have called OPAL (optimum algebra), is based on the PRORAB programming systeq2 devised for operations with algebraic polynomials on the M-20 computer.
    The Poisson series were originally written as power series with complex indices (each trigonometric term had two indices). But too much machine time was required; we therefore abandoned the power-series representation and employed optimum algorithms for addition, arrangesystem, ment of like terms, sorting, and so on. This practice speeds the performance of operations with Poisson series by a factor of 20-30, and it has enabled the OPAL system tobe applied successfully for solving the primary problem in the theory of satellite motion: the computation of perturbations from the second zonal harmonic.
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