This paper presents a compact diierential formula for the rst derivative of a unit quaternion curve deened on SO(3) or S 3. The formula provides a convenient way to compute the angular velocity of a rotating 3D solid. We demonstrate the eeectiveness of this formula by deriving the diierential properties of various unit quaternion curves 4, 5, 6, 7, 8] at the curve end points.

A generalization of Lax-Hopf formula in the case when the Lagrangian depends not only on the velocity, but also on time and velocity has been provided in [15, Chen Luxi]. On the other hand, Cournot maps have been introduced and studied in [6, Aubin & Chen Luxi] for associating with terminal time and state a temporal window on which starts at least one evolution governed by a differential inclus...

Cold-target recoil-ion-momentum spectroscopy ~COLTRIMS! has been used to study single electron capture from He by Ar ions at projectile velocities between 0.2 and 1.0 a.u. Populations of 3d through 7l states on the final ion are resolved, and angular distributions are presented for separated major final channels. As the projectile velocity is raised, the reaction window is observed to spread. C...

(i) Suppose that an " infinite string " has an initial displacement   x + 1, −1 ≤ x ≤ 0  u (x, 0) = f (x) = 1 − 2x, 0 ≤ x ≤ 1/2   0, x < −1 and x > 1/2 and zero initial velocity u t (x, 0) = 0. Write down the solution of the wave equation u tt = u xx with ICs u (x, 0) = f (x) and u t (x, 0) = 0 using D'Alembert's formula. Illustrate the nature of the solution by sketching the ux-profiles y...

AIMS To study left ventricular mechanics of exercise with Doppler and tissue Doppler. METHODS AND RESULTS Twenty-one males (mean age, 26; height, 184 cm; weight, 84 kg), exercised on a bicycle, with increasing workload, with oxygen uptake, Doppler flow and tissue Doppler recordings during exercise. There was correlation between peak systolic LVOT flow and annulus velocity; R=0.72, (p<0.001) a...

Studies have shown that the limit on the updating formula of velocity in particle swarm optimization (PSO) can produce good performance. Inspired by the logic, we introduce the concept of velocity into bare bones particle swarm optimization (BBPSO), which doesn’t consider the velocity term, hence no constraint on velocity. The velocity term is an additional restriction, and thus it doesn’t dama...

knowledge of the aerodynamic properties of agricultural materials is needed in equip-ment design for operations such as pneumatic conveying in loading/unloading operations of corn silage into/from silos. while considerable information is available on seed grains, little is known about the aerodynamic behavior of corn (zea mays l.) silage. in this re-search, the weighed mean terminal velocity of...