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We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to…
General Successive Convex Relaxation Methods (SRCMs) can be used to compute the convex hull of any compact set, in an Euclidean space, described by a system of quadratic inequalities and a compact convex set which is not very complicated.…
General Successive Convex Relaxation Methods (SRCMs) can be used to compute the convex hull of any compact set, in an Euclidean space, described by a system of quadratic inequalities and a compact convex set which is not very complicated.…
This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as…
Tetrahedral configurations of spacecraft on unperturbed heliocentric orbits allow for highly precise observations of small spatial changes in the gravitational field, especially those affecting the gravity gradient tensor (GGT). The…
This article studies the time-optimal path planning problem for a convexified Reeds-Shepp (CRS) vehicle on a unit sphere, capable of both forward and backward motion, with speed bounded in magnitude by 1 and turning rate bounded in…
This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…
The solar gravitational lens (SGL) provides a factor of $10^{11}$ amplification for viewing distant point sources beyond our solar system. As such, it may be used for resolved imaging of extended sources, such as exoplanets, not possible…
Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly-averaged equations of motion. The coupled perturbations affect the…
The classical Laplace surface defines the location of circular particle orbits that do not undergo nodal precession around a planet with some obliquity. Close to the planet the surface coincides with the equator of the planet, while far…
This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground…
Advanced diffractive films may afford advantages over passive reflective surfaces for a variety space missions that use solar or laser in-space propulsion. Three cases are compared: Sun-facing diffractive sails, Littrow diffraction…
We study the spatial isosceles three-body problem from the perspective of Symplectic Dynamics. For certain choices of mass ratio, angular momentum, and energy, the dynamics on the energy surface is equivalent to a Reeb flow on the tight…
We study a simple analytic solution to Einstein's field equations describing a thin spherical shell consisting of collisionless particles in circular orbit. We then apply two independent criteria for the identification of circular orbits,…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Beyond the Sun-Earth line, spacecraft equipped with various solar telescopes are intended to be deployed at several different vantage points in the heliosphere to carry out coordinated, multi-view observations of the Sun and its dynamic…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis…
Attitude Dynamics of a rigid artificial satellite subject to gravity gradient and Lorentz torques in a circular orbit is considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the…