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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Symbol-oriented failure analysis in multicomponent systems
Computer oriented error analysis of electrical circuits and nonlinear system performance
An algorithm for deriving the equations of mathematical physics by symbolic manipulation.
Algorithm for Navier-Stokes and continuity equations used to derive curvilinear coordinate system
Design using symbolic topological equations.
Network synthesis technique applied to structural dynamics design, using topological formulas to express systems response transfer functions
Digital computer generation of symbolic Liapunov functions
Digital computer generation of system stability Liapunov functions for ninth order spacecraft attitude control
An attempt to solve differential equations symbolically
Writing programs in interactive FORMAC language to implement Picard iteration in solving systems of ordinary differential equations
The use of computer aided symbolic mathematics to explore the higher derivatives of Bellman's equation
Using FORMAC system to solve optimal control problem of behavior of higher space derivatives of optimal value function along optimal trajectory
Computer program documentation model compiler. A symbolic input processor interfaced with the propulsion analysis program, volume 1
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Topological formulation of symbolic network functions and sensitivity analysis of active networks
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Symbol synchronizer assembly instability study, part 2
Data processing to develop a third-order phase model and to translate all such processed data to the frequency realm for further analysis was described. The frequency study yields a long frequency modulation (FM) drift sinusoid (1600-sec period), an impressed secondary drift wave with a period of about 116 sec, and a set of even harmonics of twice the ramp period-the latter arising from, and used to modify, the phase detector model. The result is applied secondarily to estimate the strong-signal SSA phase detector response "out-of-lock." Finally, the main drift components are verified against all available data, and the result is used to estimate minimum lock conditions and the SSA drift effect under normal operating modes. The instability problem appears marginally resolvable if the acquisition technique is modified.
In-flight research applications of an analog computer and symbol generator to determine display and control requirements for VTOL instrument landings
This paper describes the design and application of an airborne analog computer and display generator. The system was developed as an aid to investigate the interaction of display system complexity and control system complexity on pilot rating and performance for VTOL aircraft instrument landings.
A generalization of minimum-shift-keying /MSK/-type signaling based upon input data symbol pulse shaping
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Symbolic Laplace transforms of special functions
A MACSYMA implementation of the Laplace transform for special functions is described. The generalized hypergeometric functions are used as a basis for the representation of approximately fifty special functions. Only a relatively small number of formulas that generally involve generalized hypergeometric functions are utilized for the integration stage. A sample of actual examples and their timing is provided.
A special purpose symbolic manipulation program for the derivation of the equations of motion for large flexible structures
This paper outlines a computer program especially tailored to the task of deriving explicit equations of motion for structures with point-connected substructures. The special purpose program is written in FORTRAN and is designed for performing the specific algebraic operations encountered in the derivation of explicit equations of motion. The derivation is by the Lagrangian approach. Using an orderly kinematical procedure and a discretization and/or truncation scheme, it is possible to write the kinetic and potential energy of each substructure in a compact vector-matrix form. Then, if each element of the matrices and vectors encountered in the kinetic and potential energy is a known algebraic expression, the computer program performs the necessary operations to evaluate the kinetic and potential energy of the system explicitly. Lagrange's equations for small motions about equilibrium can be deduced directly from the explicit form of the system kinetic and potential energy.
Derivation of the equations of motion for complex structures by symbolic manipulation
This paper outlines a computer program especially tailored to the task of deriving explicit equations of motion for structures with point-connected substructures. The special purpose program is written in FORTRAN and is designed for performing the specific algebraic operations encountered in the derivation of explicit equations of motion. The derivation is by the Lagrangian approach. Using an orderly kinematical procedure and a discretization and/or truncation scheme, it is possible to write the kinetic and potential energy of each substructure in a compact vector-matrix form. Then, if each element of the matrices and vectors encountered in the kinetic and potential energy is a known algebraic expression, the computer program performs the necessary operations to evaluate the kinetic and potential energy of the system explicitly. Lagrange's equations for small motions about equilibrium can be deduced directly from the explicit form of the system kinetic and potential energy.
Symbolic Solution of Linear Differential Equations
An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.
Asymptotic matching by the symbolic manipulator MACSYMA
The delegation of the labor of calculating higher-order terms in singular perturbation (SP) expansions to a computer by the use of MACSYMA is considered. The method of matched asymptotic expansions is studied in detail for two model SP problems: a model resembling the boundary layer equation with a small parameter multiplying the highest derivatives; and a turning-point problem. It is shown that MACSYMA has successfully performed the higher-order matching in both problems.
Investigations into the shape-preserving interpolants using symbolic computation
Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines.