Engineering topics
Publications and source records attributed to Stokes, A..
A regularization of Kepler's problem due to Moser (1970) is used to stabilize the equations of motion. In other words, a particular solution of Kepler's problem is imbedded in a Liapunov stable system. Perturbations can be introduced into the stabilized equations.
A converse theorem using Liapunov functions is used to obtain upper error bounds in optimal estimates of perturbed two body problems.
A comparison theorem estimating the difference between solutions of a perturbed and unperturbed equation is obtained. This is then applied to obtain error estimates in numerical integration problems, in particular, those problems involving computation of satellite orbits. The main result is a proof of the intuitive notion that the error in numerically integrating a stable equation grows less rapidly than for an unstable equation.
An investigation was conducted with the aid of a computer graphics device at Goddard Space Flight Center to study the behavior of the invariant manifolds of a particular fourth-order equation, as a parameter in the equation is varied over the interval from 0 to 1. The equation consists of two coupled Van der Pol equations. For a small parameter value, the manifold is an asymptotically stable torus, where the flow on the torus is simply a rotation. As the value of the parameter is increased, the only thing that changes is the nature of the flow on the torus, which itself persists throughout the parameter variation. It is shown that ultimately the four periodic cycles which appear play a more significant part in the phase profile of the system than does the torus itself.