Deprit, André
Overview
Works:  46 works in 68 publications in 3 languages and 180 library holdings 

Roles:  Author 
Classifications:  Q56, 531.01517 
Publication Timeline
.
Most widely held works by
André Deprit
Compression of ephemerides by discrete Chebyshev approximations by
Andr Deprit(
Book
)
3 editions published in 1979 in English and held by 55 WorldCat member libraries worldwide
3 editions published in 1979 in English and held by 55 WorldCat member libraries worldwide
Contribution à l'étude de l'algèbre des applications linéaires continues d'un espace localement convexe séparé: théorie
de Rieszthéorie spectrale by
Andr Deprit(
Book
)
12 editions published between 1958 and 1959 in French and Undetermined and held by 39 WorldCat member libraries worldwide
12 editions published between 1958 and 1959 in French and Undetermined and held by 39 WorldCat member libraries worldwide
Edición de documentos en LATEX by
Andr Deprit(
Book
)
3 editions published in 1990 in Spanish and held by 13 WorldCat member libraries worldwide
3 editions published in 1990 in Spanish and held by 13 WorldCat member libraries worldwide
Mécanique rationnelle by
Andr Deprit(
Book
)
3 editions published between 1967 and 1970 in French and English and held by 9 WorldCat member libraries worldwide
3 editions published between 1967 and 1970 in French and English and held by 9 WorldCat member libraries worldwide
A manifold of periodic orbits by
Andr Deprit(
Book
)
1 edition published in 1967 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1967 in English and held by 4 WorldCat member libraries worldwide
Natural orbits of the first kind in the restricted problem by
Andr Deprit(
Book
)
2 editions published in 1967 in English and held by 4 WorldCat member libraries worldwide
Lindstedt's method is applied to expand analytically the natural families of periodic orbits of the first kind in the restricted problem of three bodies. The mass ratio is kept as a literal variable; the series proceed in the powers of Hill's ratio of periods. They cover all four cases at once, namely the direct or retrograde orbits for either inferior planets or for satellites. When the mass ratio is given a numerical value, the expansions contain less terms and thus can be carried up to degree 17 within a 32K core of an IBM 7094. For the system SunJupiter, the initial conditions provided by the series have been corrected to yield the beginnings of all four natural families, and the characteristic exponents have been computed. Comparison between the values computed out of the series and their improvement by numerical integrations and successive variational corrections show that, within an accuracy of one part in ten thousand, the series represent moderately well even the orbit of J VIII; the retrograde planetary orbits are fairly well covered up to 90% of the distance from SunJupiter, whereas the direct planetary orbits are covered only up to 60% of that distance. (Author)
2 editions published in 1967 in English and held by 4 WorldCat member libraries worldwide
Lindstedt's method is applied to expand analytically the natural families of periodic orbits of the first kind in the restricted problem of three bodies. The mass ratio is kept as a literal variable; the series proceed in the powers of Hill's ratio of periods. They cover all four cases at once, namely the direct or retrograde orbits for either inferior planets or for satellites. When the mass ratio is given a numerical value, the expansions contain less terms and thus can be carried up to degree 17 within a 32K core of an IBM 7094. For the system SunJupiter, the initial conditions provided by the series have been corrected to yield the beginnings of all four natural families, and the characteristic exponents have been computed. Comparison between the values computed out of the series and their improvement by numerical integrations and successive variational corrections show that, within an accuracy of one part in ten thousand, the series represent moderately well even the orbit of J VIII; the retrograde planetary orbits are fairly well covered up to 90% of the distance from SunJupiter, whereas the direct planetary orbits are covered only up to 60% of that distance. (Author)
Construction of orbits asymptotic to a periodic orbit by
Andr Deprit(
Book
)
2 editions published in 1968 in English and held by 3 WorldCat member libraries worldwide
In the immediate neighborhood of an unstable periodic orbit, the families of orbits asymptotic to it may be expanded in power series of an orbital parameter, the coefficients being successive variations of increasing order from the generating orbit. When the dynamical system is Hamiltonian, conservative and with two degrees of freedom, the intrinsic components of these variations are shown to be solutions of a recurrent sequence consisting at each step of a nonhomogeneous Hill's equation for the normal displacements and of a quadrature for the tangential components. Accordingly, Floquet's theory reduces the construction of the asymptotic series to a chain of routine operations, like trigonometric interpolations and elementary primitives. In the case of the restricted problem of three bodies, even the development of the force function about the periodic orbit can be implemented automatically on a computer. (Author)
2 editions published in 1968 in English and held by 3 WorldCat member libraries worldwide
In the immediate neighborhood of an unstable periodic orbit, the families of orbits asymptotic to it may be expanded in power series of an orbital parameter, the coefficients being successive variations of increasing order from the generating orbit. When the dynamical system is Hamiltonian, conservative and with two degrees of freedom, the intrinsic components of these variations are shown to be solutions of a recurrent sequence consisting at each step of a nonhomogeneous Hill's equation for the normal displacements and of a quadrature for the tangential components. Accordingly, Floquet's theory reduces the construction of the asymptotic series to a chain of routine operations, like trigonometric interpolations and elementary primitives. In the case of the restricted problem of three bodies, even the development of the force function about the periodic orbit can be implemented automatically on a computer. (Author)
The trojan manifold in the system EarthMoon by
Andr Deprit(
Book
)
1 edition published in 1967 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1967 in English and held by 3 WorldCat member libraries worldwide
Natural families of periodic orbits by
Andr Deprit(
Book
)
1 edition published in 1966 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 3 WorldCat member libraries worldwide
Computerized expansions in elliptic motion by
Andr Deprit(
Book
)
2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide
The functions of the Keplerian elliptic motion are expanded with respect to mean anomaly and the eccentricity by applying Poincare's method of continuation in a direct manner to the equations of motion. Two algorithms are proposed; both lead to programs by which the classical expansions are constructed symbolically and automatically on a computer in double precision arithmetic. Even to as high a degree as 30 in the eccentricity, the procedures are remarkably swift. Special care is taken here in describing significant error controls at each step of the recurrences
2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide
The functions of the Keplerian elliptic motion are expanded with respect to mean anomaly and the eccentricity by applying Poincare's method of continuation in a direct manner to the equations of motion. Two algorithms are proposed; both lead to programs by which the classical expansions are constructed symbolically and automatically on a computer in double precision arithmetic. Even to as high a degree as 30 in the eccentricity, the procedures are remarkably swift. Special care is taken here in describing significant error controls at each step of the recurrences
La géométrie affiné et ses structures by
Andr Deprit(
Book
)
3 editions published between 1962 and 1966 in French and held by 3 WorldCat member libraries worldwide
3 editions published between 1962 and 1966 in French and held by 3 WorldCat member libraries worldwide
Stability of the triangular Lagrangian points by
Andr Deprit(
Book
)
1 edition published in 1966 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 3 WorldCat member libraries worldwide
Periodic Trojan orbits for the resonace 1/12 by
Andr Deprit(
Book
)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
Birkhoff's normalization(
Book
)
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Asymptotic representation of the cycle of Van der Pol's equation for small damping coefficients by
Andr Deprit(
Book
)
1 edition published in 1967 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1967 in English and held by 2 WorldCat member libraries worldwide
THE HALOING EFFECT OF THE THIRD INTEGRAL(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Whether Contopoulos' galactic system is separable (unlikely) or not (likely), the fact is that there exists a vicinity of the equilibrium in which numerical integration of high accuracy cannot separate the system from its image through a Birkhoff's normalization of high order. To all practical purposes, Stellar Dynamics is then justified in pretending that the model is, in that region, structured by a socalled third integral. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Whether Contopoulos' galactic system is separable (unlikely) or not (likely), the fact is that there exists a vicinity of the equilibrium in which numerical integration of high accuracy cannot separate the system from its image through a Birkhoff's normalization of high order. To all practical purposes, Stellar Dynamics is then justified in pretending that the model is, in that region, structured by a socalled third integral. (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)
Numerical integration of an orbit and its concomitant variations by recurrent power series(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library 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 1 WorldCat member library 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)
Asymptotic representation of the cycle of van der pol's equation for small damping coefficients(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The limit cycle of Van der Pol's equation is expanded as a power series of the damping coefficient epsilon, the coefficients being finite trigonometric sums with the time as argument. Because the development was implemented in a fully automatic way on a computer, it has been pushed to a high power of epsilon. Hence, for epsilon as large as 0.75, the estimates given by the series for the amplitude and the period agree to 15 decimal places with their correct values computed on integrating by recurrent power series Van der Pol's equation and its associated variational equation. When epsilon reaches 1.75, the agreement is still within 0.001. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The limit cycle of Van der Pol's equation is expanded as a power series of the damping coefficient epsilon, the coefficients being finite trigonometric sums with the time as argument. Because the development was implemented in a fully automatic way on a computer, it has been pushed to a high power of epsilon. Hence, for epsilon as large as 0.75, the estimates given by the series for the amplitude and the period agree to 15 decimal places with their correct values computed on integrating by recurrent power series Van der Pol's equation and its associated variational equation. When epsilon reaches 1.75, the agreement is still within 0.001. (Author)
NORMALIZATION AT L4(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
Birkhoff's normalization about a stable equilibrium for a conservative Hamiltonian system with two degrees of freedom can be implemented in a direct way: the necessary canonical transformation is built up explicitly, without inversions, by the method of undetermined coefficients. This procedure has been programmed symbolically for an electronic computer. It has been applied up to order 13 to the equilateral center of libration in the Restricted Problem of Three Bodies for the system EarthMoon. The validity of the normalization is discussed for this case. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
Birkhoff's normalization about a stable equilibrium for a conservative Hamiltonian system with two degrees of freedom can be implemented in a direct way: the necessary canonical transformation is built up explicitly, without inversions, by the method of undetermined coefficients. This procedure has been programmed symbolically for an electronic computer. It has been applied up to order 13 to the equilateral center of libration in the Restricted Problem of Three Bodies for the system EarthMoon. The validity of the normalization is discussed for this case. (Author)
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Related Identities
 Poplarchek, Walter
 Pickard, Henry
 Naval Research Laboratory (U.S.). Space Sciences Division Technical Staff
 BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
 Henrard, Jacques
 Ferrer, Sebastián
 Boeing Scientific Research Laboratories
 Elipe, A. (Antonio)
 Rouche, Nicolas
 Rom, Arnold
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Associated Subjects
AsteroidsOrbits Asymptotic expansions Celestial mechanics Chebyshev approximation Chebyshev polynomials Combinatorial dynamics Differentiable dynamical systems Differential equations, NonlinearAsymptotic theory Ephemerides Functional analysis Lagrangian points Lie groups Mechanics, Analytic Orbits Polynomials Stability Threebody problem Twobody problem