0 (r sin θ + z)r dz dr dθ (b) Let T be the solid ball of radius 1 centered at (2, 0, 0). Set up, but do not evaluate, a triple integral in spherical coordinates which computes the moment of inertia of T around the z-axis. Hint: First consider the change of variables u = x − 2, v = y, w = z. Solution. After the change of variables, the sphere takes the form u+v+w = 1, and the z-axis becomes the ...

The W. M. Keck Observatory Adaptive Optics (AO) team recently celebrated a milestone first AO-corrected image with the new Laser Guide Star (LGS) system. This paper details focus and pointing changes implemented for the LGS AO system. The combination of variable sodium altitude, elevation-dependent distance to the LGS, off-axis projection, and equipment flexure require both focus and pointing a...

Geometries for measuring radome characteristics can usually be split into two categories. The first category always has the antenna inside the radome pointing along the range axis. The second category has the antenna maintaining a fixed relationship with respect to the radome during each scan of data. A facility can generally be designed to minimize measurement errors in one of the two geometri...

ABSTRACT We provide evidence that the sunward-propagating half of solar wind electron halo distribution evolves without scattering in inner heliosphere. assume particles conserve their total energy and magnetic moment, perform a ‘Liouville mapping’ on pitch angle distributions measured by Parker Solar Probe SPAN-E instrument. Namely, we show are consistent with Liouville’s theorem if an appropr...

A new approach for spacecraft maneuver based upon constraint dynamics and tracking control laws is presented in this paper. For high precision pointing requirement on spacecraft maneuver, a desired trajectory is prescribed upon which a constraint dynamic system is constructed. A reference model system governed by constraint force is used to build the associated control laws for actual system. S...

[1] We investigate magnetic field oscillations near the planetary rotation period in Saturn’s magnetosphere observed during the initial near‐equatorial phase of the Cassini mission. Phase determinations on 28 periapsis passes during this ∼2 year interval display pronounced nonrandom “jitter” relative to the ∼10.8 h modulations in the dominant southern Saturn kilometric radiation (SKR) emissions...

A variant on the electroor magnetostatic boundary value problem arises in accelerator physics, where a specified field, say B(0, 0, z), is desired along the z axis. In general there exist static fields B(x, y, z) that reduce to the desired field on the axis, but the “boundary condition” B(0, 0, z) is not sufficient to insure a unique solution. For example, find a field B(x, y, z) that reduces to

This paper reports the first design and its simulation and experimental results of a CMOS z-axis microactuator that utilizes the vertical electrostatic forces existing between multi-conductor comb fingers. The measured maximum displacement of the z-axis microactuator is 3.5 μm, and resonant frequency 6.17 kHz, which are in good agreement with the field simulation and the behavioral simulation r...