A geometric approach to three-dimensional hipped bipedal robotic walking

This paper presents a control law that results in stable walking for a three-dimensional bipedal robot with a hip. To obtain this control law, we utilize techniques from geometric reduction, and specifically a variant of Routhian reduction termed functional Routhian reduction, to effectively decouple the dynamics of the three-dimensional biped into its sagittal and lateral components. Motivated by the decoupling afforded by functional Routhian reduction, the control law we present is obtained by combining three separate control laws: the first shapes the potential energy of the sagittal dynamics of the biped to obtain stable walking gaits when it is constrained to the sagittal plane, the second shapes the total energy of the walker so that functional Routhian reduction can be applied to decoupling the dynamics of the walker for certain initial conditions, and the third utilizes an output zeroing controller to stabilize to the surface defining these initial conditions. We numerically verify that this method results in stable walking, and we discuss certain attributes of this walking gait

F-15 inlet engine test techniques and distortion methodologies studies. Volume 9: Stability audits

Stability audit plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

F-15 inlet/engine test techniques and distortion methodologies studies. Volume 2: Time variant data quality analysis plots

Time variant data quality analysis plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

F-15 inlet/engine test techniques and distortion methodologies studies. Volume 7: Cross correlation functions.

Cross correlation function plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

F-15 inlet/engine test techniques and distortion methodologies studies. Volume 3: Power spectral density plots

Power spectral density plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

F-15 inlet/engine test techniques and distortion methodologies studies. Volume 8: Cross spectral density plots

Cross spectral density plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

F-15 inlet/engine test techniques and distortion methodologies studies. Volume 4: Autocorrelation functions

Autocorrelation function plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

F-15 inlet/engine test techniques and distortion methodologies studies. Volume 5: Effect of filter cutoff frequency on turbulence plots

The effect of filter cutoff frequency on turbulence plots were used to determine if peak distortion data taken from a subscale inlet model can be used to predict peak distortion levels for a full scale flight test vehicle

Rotation and Neoclassical Ripple Transport in ITER

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria with toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver (SFINCS). These calculations fully account for $E_r$, flux surface shaping, multiple species, magnitude of ripple, and collisionality rather than applying approximate analytic NTV formulae. As NTV is a complicated nonlinear function of $E_r$, we study its behavior over a plausible range of $E_r$. We estimate the toroidal flow, and hence $E_r$, using a semi-analytic turbulent intrinsic rotation model and NUBEAM calculations of neutral beam torque. The NTV from the $\rvert n \rvert = 18$ ripple dominates that from lower $n$ perturbations of the TBMs. With the inclusion of FIs, the magnitude of NTV torque is reduced by about 75% near the edge. We present comparisons of several models of tangential magnetic drifts, finding appreciable differences only for superbanana-plateau transport at small $E_r$. We find the scaling of calculated NTV torque with ripple magnitude to indicate that ripple-trapping may be a significant mechanism for NTV in ITER. The computed NTV torque without ferritic components is comparable in magnitude to the NBI and intrinsic turbulent torques and will likely damp rotation, but the NTV torque is significantly reduced by the planned ferritic inserts

Radial mode structure of curvature-driven instabilities in EBT

Viewgraphs describe the theoretical treatment of the radial mode structure of plasma instabilities in the Elmo Bumpy Torus. The calculation retains nonlocal structure of the modes, connects inner and outer ring regions together, uses a self-consistent finite ..beta.., includes the relativistic effects for the hot electron ring, and examines a wide range of parameters. (WRF