BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
Overview
Works:  166 works in 166 publications in 1 language and 171 library holdings 

Classifications:  QB351, 
Publication Timeline
.
Most widely held works by
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
The roche coordinates and their use in celestial mechanics or hydrodynamics by
Zdeněk Kopal(
Book
)
1 edition published in 1969 in English and held by 3 WorldCat member libraries worldwide
The air of the report will be to introduce a new system of curvilinear coordinateshereafter referred to as Roche coordinatesin which spheres of constant radius are replaced by equipotential surfaces of a rotating gravitational dipole (which consists of two discrete points of finite mass, revolving around their common center of gravity); while the remaining coordinates are orthogonal to the equipotentials. It will be shown that the use of such coordinates offers a new method of approach to the solution of certain problems of particle dynamics (such as, for instance, the construction of certain types of trajectories in the restricted problem of three bodies); as well as of the hydrodynamics of gas streams in close binary systems, in which the equipotential surfaces of their components distorted by axial rotation and mutual tidal interaction constitute essential boundary conditions. (Author)
1 edition published in 1969 in English and held by 3 WorldCat member libraries worldwide
The air of the report will be to introduce a new system of curvilinear coordinateshereafter referred to as Roche coordinatesin which spheres of constant radius are replaced by equipotential surfaces of a rotating gravitational dipole (which consists of two discrete points of finite mass, revolving around their common center of gravity); while the remaining coordinates are orthogonal to the equipotentials. It will be shown that the use of such coordinates offers a new method of approach to the solution of certain problems of particle dynamics (such as, for instance, the construction of certain types of trajectories in the restricted problem of three bodies); as well as of the hydrodynamics of gas streams in close binary systems, in which the equipotential surfaces of their components distorted by axial rotation and mutual tidal interaction constitute essential boundary conditions. (Author)
The shape of the moon as deduced from the orbiter determination of its gravitational field(
Book
)
1 edition published in 1966 in English and held by 2 WorldCat member libraries worldwide
Preliminary values of the lunar gravity field as obtained from an analysis of the tracking data of Lunar Orbiter 1 are used to express the basic features of the figure of the Moon. Some tentative conclusions are drawn regarding the homogeneity, the nonhydrostatic form, and the solidity of the lunar globe. (Author)
1 edition published in 1966 in English and held by 2 WorldCat member libraries worldwide
Preliminary values of the lunar gravity field as obtained from an analysis of the tracking data of Lunar Orbiter 1 are used to express the basic features of the figure of the Moon. Some tentative conclusions are drawn regarding the homogeneity, the nonhydrostatic form, and the solidity of the lunar globe. (Author)
On a heat and mass transfer problem with two moving boundaries by
J. C. Y Koh(
Book
)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
The heat and mass transfer problem in a passive transpiration cooling system involving two moving boundaries is formulated. A numerical calculation scheme and computer program are developed to solve the problem. Computations are performed for the case of porous tungsten infiltrated with copper exposed to an environment of high pressure and high heat flux. The effects of porosities and the radius of curvature on the thermal response and infiltrant recession are shown. (Author)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
The heat and mass transfer problem in a passive transpiration cooling system involving two moving boundaries is formulated. A numerical calculation scheme and computer program are developed to solve the problem. Computations are performed for the case of porous tungsten infiltrated with copper exposed to an environment of high pressure and high heat flux. The effects of porosities and the radius of curvature on the thermal response and infiltrant recession are shown. (Author)
Numerical integration of an orbit and its concomitant variations by recurrent power series(
Book
)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
Power series expansions (with coefficients obtained by recurrence formulas) are more efficient than other integration procedures for computing concurrently an orbit and the resolvent matrix of its variational equations, in the Restricted Problem of Three Bodies. For the same requirements on accuracy, the series expansions use only about 30 per cent of the computing time of the multistep procedures, and only 12 to 15 per cent of the computing time of the RungeKuttaNystrom method. (Author)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
Power series expansions (with coefficients obtained by recurrence formulas) are more efficient than other integration procedures for computing concurrently an orbit and the resolvent matrix of its variational equations, in the Restricted Problem of Three Bodies. For the same requirements on accuracy, the series expansions use only about 30 per cent of the computing time of the multistep procedures, and only 12 to 15 per cent of the computing time of the RungeKuttaNystrom method. (Author)
Harmonic analysis of the Selenodetic Control System of the Department of Defense by T. A Bray(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The Department of Defense Selenodetic Control System 1966 (DOD66) is expressed here in terms of spherical harmonics. The coefficients obtained are different from those obtained on the basis of all previous systems. The second zonal harmonic corresponding to the DOD66 suggests the improbable hypothesis that the Moon is elongated along the axis of rotation and, in particular, that the polar diameter exceeds the equatorial diameter by about 1 kilometer. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The Department of Defense Selenodetic Control System 1966 (DOD66) is expressed here in terms of spherical harmonics. The coefficients obtained are different from those obtained on the basis of all previous systems. The second zonal harmonic corresponding to the DOD66 suggests the improbable hypothesis that the Moon is elongated along the axis of rotation and, in particular, that the polar diameter exceeds the equatorial diameter by about 1 kilometer. (Author)
Sufficient conditions connected with differential inequalities of the fourth order(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
Internal structure of the moon by
Zdeněk Kopal(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
The internal structure of the moon and its evolution are discussed. Some topics considered are: hydrostatic equilibrium; thermal history of the moon; stress history of the moon; possible convection in lunar interior; chemical composition of the moon; lunar exosphere
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
The internal structure of the moon and its evolution are discussed. Some topics considered are: hydrostatic equilibrium; thermal history of the moon; stress history of the moon; possible convection in lunar interior; chemical composition of the moon; lunar exosphere
On evaluation of warranty assurance when life has a weibull distribution(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
A two parameter Weibull model with neither parameter known is assumed for failure time. A value is specified for the probability that no failures, in a lot of identically distributed components yet to be manufactured, will occur before the expiration of the warranty period. The warranty period, which must satisfy an assurance criterion at the prescribed probability level regardless of the true parameter values within the distribution, is to be calculated from a small preliminary sample of life lengths. An expression for the warranty period is derived as a function of the ordered observations and is determined only by the lot size, the sample size and the prescribed assurance level. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
A two parameter Weibull model with neither parameter known is assumed for failure time. A value is specified for the probability that no failures, in a lot of identically distributed components yet to be manufactured, will occur before the expiration of the warranty period. The warranty period, which must satisfy an assurance criterion at the prescribed probability level regardless of the true parameter values within the distribution, is to be calculated from a small preliminary sample of life lengths. An expression for the warranty period is derived as a function of the ordered observations and is determined only by the lot size, the sample size and the prescribed assurance level. (Author)
Characteristic exponents at l sub 4 in the elliptic restricted problem(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
The systems considered here are Hamiltonian, linear with periodic coefficients and depending on a small parameter. A perturbation method based on Lie transforms is proposed to develop the characteristic exponents of the monodromy matrix in power series of the small parameter. The algorithm is applied to the triangular Lagrangian solutions in the elliptic restricted problem. The principal parts of their characteristic exponents have been obtained in literal form as irrational functions of the mass ratio. The actual calculation has been automated by means of a package of subroutines coded to process Echeloned Series. The strong stability of the Lagrangian solutions is discussed in relation to the eccentricity of the primaries. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
The systems considered here are Hamiltonian, linear with periodic coefficients and depending on a small parameter. A perturbation method based on Lie transforms is proposed to develop the characteristic exponents of the monodromy matrix in power series of the small parameter. The algorithm is applied to the triangular Lagrangian solutions in the elliptic restricted problem. The principal parts of their characteristic exponents have been obtained in literal form as irrational functions of the mass ratio. The actual calculation has been automated by means of a package of subroutines coded to process Echeloned Series. The strong stability of the Lagrangian solutions is discussed in relation to the eccentricity of the primaries. (Author)
Programming under uncertainty: the solution set(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
In a previous paper (AD612 896), the author described and characterized the equivalent convex program of a twostage linear program under uncertainty. It was proven that the solution set of a linear program under uncertainty is convex and derived explicit expressions for this set for some particular cases. The main result of this paper is to show that the solution set is not only convex but also polyhedral. It is also shown that the equivalent convex program of a multistage programming under uncertainty problem is of the form: Minimize a convex function subject to linear constraints. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
In a previous paper (AD612 896), the author described and characterized the equivalent convex program of a twostage linear program under uncertainty. It was proven that the solution set of a linear program under uncertainty is convex and derived explicit expressions for this set for some particular cases. The main result of this paper is to show that the solution set is not only convex but also polyhedral. It is also shown that the equivalent convex program of a multistage programming under uncertainty problem is of the form: Minimize a convex function subject to linear constraints. (Author)
Random variables with independent binary digits(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Let X = .b1b2b3 ... be a random variable with independent binary digits bn taking values 0 or 1 with probabilities pn and qn. When does X have a density function. A continuous density function. A singular distribution. This note proves that the distribution X is singular is and only if the tail of the series Summation (log(pn/qn)) squared diverges, and that X has a density that is positive on some interval if and only if log(pn/qn) is a geometric sequence with ratio 1/2 for n greater than some k, and in that case the fractional part of (2 to the power k)X has an exponential density (increasing or decreasing with the uniform density a special case). It gives a sufficient condition for X to have a density, (Summation log (2 max (pn, qn))converges), but unless the tail of the sequence log(pn/qn) is geometric, ratio 1/2, the density is a weird one that vanishes at least once in every interval. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
Let X = .b1b2b3 ... be a random variable with independent binary digits bn taking values 0 or 1 with probabilities pn and qn. When does X have a density function. A continuous density function. A singular distribution. This note proves that the distribution X is singular is and only if the tail of the series Summation (log(pn/qn)) squared diverges, and that X has a density that is positive on some interval if and only if log(pn/qn) is a geometric sequence with ratio 1/2 for n greater than some k, and in that case the fractional part of (2 to the power k)X has an exponential density (increasing or decreasing with the uniform density a special case). It gives a sufficient condition for X to have a density, (Summation log (2 max (pn, qn))converges), but unless the tail of the sequence log(pn/qn) is geometric, ratio 1/2, the density is a weird one that vanishes at least once in every interval. (Author)
THE NUMBER OF PLANAR TREES(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
By a planar tree is meant a realization of a tree in the plane, and by an isomorphism between two planar trees is meant a mapping which is not only an isomorphism in the usual sense of trees but which also preserves the clockwise cyclic order of edges about each node. Explicit formulae are given for each of the following: (1) the number of nonisomorphic unrooted planar trees with n edges, (2) the number of nonisomorphic rooted planar trees with n edges, and (3) the number of nonisomorphic rooted planar trees with n edges such that the root is incident on exactly k edges, of which one is distinguished. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
By a planar tree is meant a realization of a tree in the plane, and by an isomorphism between two planar trees is meant a mapping which is not only an isomorphism in the usual sense of trees but which also preserves the clockwise cyclic order of edges about each node. Explicit formulae are given for each of the following: (1) the number of nonisomorphic unrooted planar trees with n edges, (2) the number of nonisomorphic rooted planar trees with n edges, and (3) the number of nonisomorphic rooted planar trees with n edges such that the root is incident on exactly k edges, of which one is distinguished. (Author)
On the third integral of the galaxy by
Constantine L Goudas(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
It is shown here that the 'third integral' of the galaxy, whenever its constant is conserved, defines the same surface as the Hamiltonian, and thus does not constitute any new integral, but a function of the already known integral of energy. In particular, the 'third integral' and the Hamiltonian are found to possess collinear gradients, in accordance with Poincare's theorem concerning the characteristic exponents in systems with multiple integrals. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
It is shown here that the 'third integral' of the galaxy, whenever its constant is conserved, defines the same surface as the Hamiltonian, and thus does not constitute any new integral, but a function of the already known integral of energy. In particular, the 'third integral' and the Hamiltonian are found to possess collinear gradients, in accordance with Poincare's theorem concerning the characteristic exponents in systems with multiple integrals. (Author)
A lipschitzian characterization of convex polyhedra(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
The Hausdorff distance between parallel crosssections of a closed convex polyhedron (whether bounded or not) possesses a Lipschitzian property. Moreover, this property characterizes convex polyhedra among the class of closed convex sets. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
The Hausdorff distance between parallel crosssections of a closed convex polyhedron (whether bounded or not) possesses a Lipschitzian property. Moreover, this property characterizes convex polyhedra among the class of closed convex sets. (Author)
Characterization of geometric and exponential distributions(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
In two works T.S. Ferguson examines the classes of independent random variables X and Y such that min(X, Y) is independent of X  Y. In one work he shows that if X (or Y) has a discrete part, then X and Y are geometric random variables. In the other work it is shown that if X and Y are absolutely continuous, then they are exponential random variables. The present author intends to complete this investigation by showing that the result of Ferguson holds even if X and Y are possibly singular
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
In two works T.S. Ferguson examines the classes of independent random variables X and Y such that min(X, Y) is independent of X  Y. In one work he shows that if X (or Y) has a discrete part, then X and Y are geometric random variables. In the other work it is shown that if X and Y are absolutely continuous, then they are exponential random variables. The present author intends to complete this investigation by showing that the result of Ferguson holds even if X and Y are possibly singular
Birkhoff's normalization(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Birkhoff's normalizing canonical transformation at an equilibrium of elliptic type with no internal resonance can be built explicitly and recursively, without partial inversions or substitutions, by means of Lie transforms. Invariant sections and ordinary families of periodic orbits for truncated normalized systems are analyzed in detail. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Birkhoff's normalizing canonical transformation at an equilibrium of elliptic type with no internal resonance can be built explicitly and recursively, without partial inversions or substitutions, by means of Lie transforms. Invariant sections and ordinary families of periodic orbits for truncated normalized systems are analyzed in detail. (Author)
The air forces on a missile near a bomb blast from the motion of the silo walls(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
To investigate the pressure waves on a missile in a silo due to the lateral acceleration of the silo walls under a nearby bomb blast, the two dimensional wave equation is solved for the air flow in the region between two coaxial cylinders under a prescribed motion of the outer cylinder normal to its axis. The velocity potential is in the form of a convolution integral with the velocity of the outer cylinder and an impulse function in the form of an eigenfunction expansion of first order Bessel functions, sines, and cosines. Convergence is improved by subtracting from each term its asymptotic form and adding the closed form expression for the asymptotic expansion. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
To investigate the pressure waves on a missile in a silo due to the lateral acceleration of the silo walls under a nearby bomb blast, the two dimensional wave equation is solved for the air flow in the region between two coaxial cylinders under a prescribed motion of the outer cylinder normal to its axis. The velocity potential is in the form of a convolution integral with the velocity of the outer cylinder and an impulse function in the form of an eigenfunction expansion of first order Bessel functions, sines, and cosines. Convergence is improved by subtracting from each term its asymptotic form and adding the closed form expression for the asymptotic expansion. (Author)
The precession and nutation of deformable bodies. v: equations of motion for spheroidal deformation(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
The general form of the Eulerian equations for the precession and nutation of deformable bodies, is particularized for the case in which the deformation is characterized by spheroidal symmetry. This assumption (which is sufficiently general to embrace most cases of astronomical interest) enables one to separate the angular and radial variables in the volume integrals contained as coefficients of the deformation terms in the equations of motion. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
The general form of the Eulerian equations for the precession and nutation of deformable bodies, is particularized for the case in which the deformation is characterized by spheroidal symmetry. This assumption (which is sufficiently general to embrace most cases of astronomical interest) enables one to separate the angular and radial variables in the volume integrals contained as coefficients of the deformation terms in the equations of motion. (Author)
Magnetic compass deviations produced by magnetic loads by Theodore P Higgins(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
The purpose of this note is to give the method for calculating the perturbation introduced into a uniform magnetic field by the presence of an unmagnetized magnetic ellipsoid. The immediate application is the determination of the error introduced into the reading flux meters aboard an aircraft by the presence of a soft iron load. Although the ellipsoid is not the ideal shape for the load, it is the most general shape for which the boundary can be expressed in terms of a constant value of a single coordinate in a coordinate system which is separable. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
The purpose of this note is to give the method for calculating the perturbation introduced into a uniform magnetic field by the presence of an unmagnetized magnetic ellipsoid. The immediate application is the determination of the error introduced into the reading flux meters aboard an aircraft by the presence of a soft iron load. Although the ellipsoid is not the ideal shape for the load, it is the most general shape for which the boundary can be expressed in terms of a constant value of a single coordinate in a coordinate system which is separable. (Author)
Analytical lunar ephemeris. 1. definition of the main problem(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
A new set of phase variables is proposed and justified to develop automatically by computer the solar terms in Lunar Theory. The dependence of the perturbation function on the mass ratio Moon/(Earth + Moon) is completely elucidated. A recursive procedure is proposed to develop that function so as to keep explicit all its d'Alembert characteristics. The perturbation series obtained by computer is compared with Delaunay's development. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
A new set of phase variables is proposed and justified to develop automatically by computer the solar terms in Lunar Theory. The dependence of the perturbation function on the mass ratio Moon/(Earth + Moon) is completely elucidated. A recursive procedure is proposed to develop that function so as to keep explicit all its d'Alembert characteristics. The perturbation series obtained by computer is compared with Delaunay's development. (Author)
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Languages