Rigorous and formal stability of orbits about an oblate planet.
Idealized point mass motion in axisymmetric gravitational field, discussing orbital stability about oblate planet
Kyner, W. T.↗
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Results for “formal”
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A linearization tool for use with matrix formalisms of rotational dynamics.
Rotational dynamics equations in linearized matrix form applied to satellite librations in circular orbit and gyroscope motion
Likins, P. W.↗
Formal solutions for a class of stochastic pursuit-evasion games.
Linear-quadratic pursuit-evasion game with dynamics perturbed by additive white Gaussian noise, obtaining linear minimax solutions
Willman, W. W.↗
Formal Rayleigh-Schroedinger perturbation theory for both degenerate and non-degenerate energy states
Degenerate and nondegenerate energy states and wave functions formulated by Rayleigh- Schroedinger perturbation theory
Hirschfelder, J. O.↗
Formal solutions for a class of stochastic pursuit-evasion games
Linear-quadratic pursuit-evasion game with dynamics perturbed by additive white Gaussian noise, obtaining linear minimax solutions
Willman, W. W.↗
A unified formalism for position determination from various navigation measurements
Development of technique for coordinate determination of moving vehicles and unified description for extracting position information from combinations of measurements
Lee, H. Q.↗
Theory of reactive scattering. 6: Volterra equation formalism for coupled channel amplitude densities and modified wavefunctions
Volterra equation for coupled channel amplitude densities and modified wave functions
Kouri, D. J.↗
Non-partial wave treatment of reactive and non-reactive scattering Coupled integral equation formalism.
Coupled integral equations are derived for the full scattering amplitudes for both reactive and nonreactive channels. The equations do not involve any partial wave expansion and are obtained using channel operators for reactive and nonreactive collisions. These coupled integral equations are similar in nature to equations derived for purely nonreactive collisions of structureless particles. Using numerical quadrature techniques, these equations may be reduced to simultaneous algebraic equations which may then be solved.
Hayes, E. F.↗
Research in advanced formal theorem-proving techniques
The present status is summarized of a continuing research program aimed at the design and implementation of a language for expressing problem-solving procedures in several areas of artificial intelligence, including program synthesis, robot planning, and theorem proving. Notations, concepts, and procedures common to the representation and solution of many of these problems were abstracted and incorporated as features into the language. The areas of research covered are described, and abstracts of six papers that contain extensive description and technical detail of the work are presented.
Rulifson, J. F.↗
Conservation laws and preferred frames in relativistic gravity. I Preferred-frame theories and an extended PPN formalism. II - Experimental evidence to rule out preferred-frame theories of gravity.
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Will, C. M.↗
Research in advanced formal theorem-proving techniques
The results are summarised of a project aimed at the design and implementation of computer languages to aid in expressing problem solving procedures in several areas of artificial intelligence including automatic programming, theorem proving, and robot planning. The principal results of the project were the design and implementation of two complete systems, QA4 and QLISP, and their preliminary experimental use. The various applications of both QA4 and QLISP are given.
Raphael, B.↗
A formal structure for advanced automatic flight-control systems
Techniques were developed for the unified design of multimode, variable authority automatic flight-control systems for powered-lift STOL and VTOL aircraft. A structure for such systems is developed to deal with the strong nonlinearities inherent in this class of aircraft, to admit automatic coupling with advanced air traffic control, and to admit a variety of active control tasks. The aircraft being considered is the augmentor wing jet STOL research aircraft.
Meyer, G.↗
Calculation of autoionization of He and H/-/ using the projection-operator formalism
Improved calculations are reported for the first several autoionization states of the lower symmetries of He and H(-). Unshifted energies are calculated by diagonalizing QHQ using a Hylleraes basis with more terms than previously used; shifts, widths, and photoabsorption shape parameters are obtained with the additional use of exchange-approximate nonresonant continuum functions. Previous calculations of H(-) resonances are reviewed and slightly augmented by applying various nonresonant continua and correcting small errors. A comparison is made between the calculations and experimental results and is found to be very satisfactory except for the lowest 1P autoionization state of He, which is shown to need a more accurate experimental determination.
Bhatia, A. K.↗
Sakata-Taketani spin-0 theory with external field interactions - Lagrangian formalism and causal properties
To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.
Guertin, R. F.↗
Modified lattice-statics approach to dislocation calculations. I - Formalism
A modified lattice-statics method to calculate the atomic displacements associated with a screw dislocation is outlined. The model incorporates an anharmonic region wherein the forces are derived from a pair potential. Appropriate energy and force expressions are derived. The modifications necessary for the implementation of the conjugate-gradient function minimization method are also derived.
Esterling, D. M.↗
An 'adding' algorithm for the Markov chain formalism for radiation transfer
An adding algorithm is presented, that extends the Markov chain method and considers a preceding calculation as a single state of a new Markov chain. This method takes advantage of the description of the radiation transport as a stochastic process. Successive application of this procedure makes calculation possible for any optical depth without increasing the size of the linear system used. It is determined that the time required for the algorithm is comparable to that for a doubling calculation for homogeneous atmospheres. For an inhomogeneous atmosphere the new method is considerably faster than the standard adding routine. It is concluded that the algorithm is efficient, accurate, and suitable for smaller computers in calculating the diffuse intensity scattered by an inhomogeneous planetary atmosphere.
Esposito, L. W.↗
Elastic lithosphere thickness on the moon from mare tectonic features - A formal inversion
The thickness (T) of the lunar elastic lithosphere at the time (3.6 to 3.8 billion years ago) of the earliest preserved basalt flows in circular mare basins can be estimated by inverting the observed locations of extensional tectonic features in and surrounding the maria. In performing the inversion, the lithosphere is modeled as an elastic shell with a liquid interior, and the basalt load for each mare is approximated by a set of concentric cylinders. To permit solving the forward problem of placing radial limits on the positions of the rilles around a given mare, an additional parameter F, the ratio of the radial stress at the radial limits to the maximum radial stress, is introduced. T and F are chosen to give the best weighted-squares fit of the radial limits to the observations, and are used as the initial values in a linearized matrix inversion to check the resolution and estimate errors. The application of the procedure to three maria with prominent extensional features, Humorum, Orientale, and Serenitatis, gives values of T from about 40 + or - 10 to 50 + or - 10 km, and in each case the linearized matrix equation has an exact inverse.
Comer, R. P.↗
A variational approach to the question of temporal stability of equilibrium models of solar prominences. I - The formal theory
A Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences is presented. Seven quantities are derived which, by analogy to the concepts of energy, momentum, and angular momentum, are conserved under conditions corresponding to ignorable coordinates of classical mechanics. It is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigenfrequencies for the perturbation equations when numerical techniques are used. The method is capable of handling complicated spatial dependences and has internal criteria for assessing the accuracy of any given numerical convergence scheme.
Lerche, I.↗