Engineering topics
Publications and source records attributed to Broucke, R..
This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.
This article studies the relativistic theory of the motion of a particle in the presence of a uniform acceleration field. The problem is introduced as a linearization of the fundamental line element of general relativity. The linearized line element is a solution of Einstein's field equations. The equations of geodesics corresponding to this line element are solved and applied to the clock paradox problem.-
This article describes a Lorentz-like transformation between a fixed frame and an inertial frame that is free falling due to the presence of a uniform gravitation field. The application to the clock paradox problem and some connections with similar works are also discussed.
Some methods are described for the expansion of the disturbing function in planetary theory. One method uses the classical binomial expansion theorem or a successive approximation process derived from it. Another method is a direct application of the Laplace series expansions. For both methods it is proposed to first prepare the series to be manipulated by a scaling operation. These methods can be applied either in a literal or in a numerical form, or any combination of both, but they are especially designed for use on a large scale digital computer with standard Poisson series programs. No usage is made of Newcomb operators or derivatives of Laplace coefficients.
Three body problem of two heavy mass particles oscillatory motion in periodic orbits on straight line under Newtonian attraction
Adaptation of Steffensen's method of solution of both the restricted and general three-body problems in terms of power series in time to the solution of the equations of motion of N planets around the sun. The key feature of this adaptation lies in the introduction of N new variables and in the use of new relations which contain the time derivatives and can thus be treated as differential equations.
Three degree of freedom perturbed two body problem, applying theory of redundant variables to Lagrangian equations of motion
A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.
Two dimensional elliptic restricted three body problem, considering regularization mechanism and periodic collision orbits
Computer program for two body problem literal series expansions using Kepler functions with Bessel and Poisson series operation
Programming system for Poisson series manipulation on computer, writing subroutines in machine language
Orbits computation by Picard successive approximations method, discussing iterative numerical perturbation techniques
Stability of periodic orbits in elliptic restricted three body problem
Stability of periodic orbits in elliptic restricted three body problem
Independent variable changes in dynamical systems and applications to systems regularization, giving canonical and Lagrangian motion equations with tensor notation
Two-body problem symmetrization - application to atmospheric drag perturbations
Simultaneous removal of singularities of plane circular restricted three-body problem by coordinate transformation defined by conformal mapping