We consider the problem of minimizing a functional (like the area, perimeter, surface) within the class of convex bodies whose support functions are trigonometric polynomials. The convexity constraint is transformed via the Fejér-Riesz theorem on positive trigonometric polynomials into a semidefinite programming problem. Several problems such as the minimization of the area in the class of cons...

The simulation of multibody systems with rigid contacts entails the solution of nonsmooth equations of motion. The dynamics is nonsmooth because of the discontinuous nature of noninterpenetration, collision, and adhesion constraints. We propose a solver that is able to handle the simulation of multibody systems of vast complexity, with more than 100,000 colliding rigid bodies. The huge number o...

New deterministic computer simulations have been developed for studying the dynamics of large objects colliding. For various initial conditions the system may clump together forming a new object or may rotate, causing ejecta to leave the primary mass in a pattern sustaining only a short number of orbits, but promising of satellite formation. Bodies without a large central mass are not able to f...

We use a smooth particle hydrodynamics method (SPH) to simulate colliding rocky and icy bodies from cm-scale to hundreds of km in diameter, in an effort to define self-consistently the threshold for catastrophic disruption. Unlike previous efforts, this analysis incorporates the combined effects of material strength (using a brittle fragmentation model) and self-gravitation, thereby providing r...

This paper deals with the calculation of the motion and the administration of the contacts for systems with many colliding bodies of round shape and possibly large size-differences. Both two dimensional (2D) and three dimensional (3D) cases are investigated, while the efficiency of the employed algorithms is compared. For the integration of the equations of motion, standard methods are used, bu...

We present results of a ≈20 ksec X-ray observation of the Wolf-Rayet (WR) binary system WR 147 obtained with XMM-Newton. Previous studies have shown that this system consists of a nitrogen-type WN8 star plus an OB companion whose winds are interacting to produce a colliding wind shock. X-ray spectra from the pn and MOS detectors confirm the high extinction reported from IR studies and reveal ho...

The elements of a general high precision system for trajectory design and optimization for single or multiple spacecraft using one or more distinct propulsion systems, and operating in any gravitational environment within the solar system are discussed. The system architecture attempts to consolidate most all spacecraft trajectory design and optimization problems by using a single framework tha...

LetK, L be congruent regular polyhedra in R. Let g denote a rigid motion of R, that is, g(x) = Φx+τ where Φ is a 3×3 rotation matrix and τ is a translation 3-vector. The polyhedraK, g(L) are said to touch ifK∩g(L) 6= ∅ but int(K)∩int(g(L)) = ∅. Alternatively, we may think of ΦL moving toward K in the direction τ , stopping precisely when the two polyhedra collide. Let us sample the space SO3 of...

Rigid body simulations require collision detection for determining contact points between simulated bodies. Collision detection performance can become dramatically slow, if geometric models of rigid bodies have intricate inaccessible regions close to their boundaries, particularly when bodies are in close proximity. As a result, frame rates of rigid body simulations reduce significantly in the ...

Procedure cloning is an interprocedural optimization where the compiler creates specialized copies of procedure bodies. To clone a procedure, the compiler repli-cates it and then divides the incoming calls between the original procedure and the copy. By carefully partitioning the call sites, the compiler can ensure that each clone inherits an environment that allows for better code optimization...