Regularization of the Hill four-body problem with oblate bodies

Global Regularization of a Restricted Four-Body Problem

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-body problem can be regularized by using a Birk...

the problem of divine hiddenness

این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...

Regularization of the collision in the electromagnetic two-body problem.

We derive a differential equation that is regular at the collision of two equal-mass bodies with attractive interaction in the relativistic action-at-a-distance electrodynamics. We use the energy constant related to the Poincare invariance of the theory to define finite variables with finite derivatives at the collision. The collision orbits are calculated numerically using the regular equation...

Integral equations for the four-body problem

Geometry-induced Casimir suspension of oblate bodies in fluids.

We predict that a low-permittivity oblate body (disk-shaped object) above a thin metal substrate (plate with a hole) immersed in a fluid of intermediate permittivity will experience a metastable equilibrium (restoring force) near the center of the hole. Stability is the result of a geometry-induced transition in the sign of the force, from repulsive to attractive, that occurs as the disk approa...