On the Addition of the Primary Aberrations

1927 ◽  
Vol 23 (5) ◽  
pp. 584-587
Author(s):  
G. C. Steward
Keyword(s):  
Characteristic Function ◽  
Composite System ◽  
Present Note ◽  
Complete System ◽  
General Will ◽  
Simple Derivation ◽  
First Order ◽  
System A ◽  
Component Systems ◽  
General Investigation

In the application of the Characteristic Function of Hamilton, or of any allied function, to the computation of a symmetrical optical system three steps are necessary. The performance of the system as a whole must be considered, and from this it appears that the aberrations may be derived from certain ‘aberration coefficients’ which occur in the expansion of an ‘aberration function’. In the second place, relations must be obtained giving the properties of the complete system in terms of the properties of the component systems, which, in general, will be single refracting surfaces; and finally, an evaluation of the coefficients must be made for the simple system—a single surface. For the first and third of these steps reference may be made elsewhere, and also for a general investigation of the second; a simple derivation is given, in the present note, of the necessary relations between a composite system and its components in the case where first order aberrations only are considered.

High Energy Focused Ion Beam Nanoprobes: Design and Applications

2005 ◽  
Vol 908 ◽  
Author(s):  
Gary A. Glass ◽  
Bibhudutta Rout ◽  
Alexander D. Dymnikov ◽  
Elia V. Eschenazi ◽  
Richard Greco ◽  
...  
Keyword(s):  
Focused Ion Beam ◽  
Complete System ◽  
Ion Beam ◽  
Heavy Ion ◽  
High Energy ◽  
System Technology ◽  
Independent Research ◽  
Coordinated Development ◽  
Component Systems ◽  
Research Facilities

AbstractAn overview of the present state of high energy focused ion beam (HEFIB) system technology, nanoprobe system design and specific ion beam writing applications will be presented. In particular, the combination of P-beam, heavy-ion writing and ion implantation to produce microstructures in resists and silicon will be demonstrated.Heretofore, the development of HEFIB technology worldwide has progressed through a series of developments at independent research facilities, each having relatively narrow and mostly isolated, research purposes. However, a complete, versatile HEFIB nanoprobe system capable of both analysis and modification will require the combination of several component systems, each with specialized technology, and significant advances in the design of a complete system can only be expected from an effort that includes a coordinated development of the component parts.

scholarly journals Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics

2020 ◽  
Vol 10 (24) ◽  
pp. 9137
Author(s):  
Hongwen Zhang ◽  
Zhanxia Zhu
Keyword(s):  
Motion Planning ◽  
Inverse Kinematics ◽  
Random Trees ◽  
Space Robot ◽  
Initial Configuration ◽  
First Order ◽  
System A ◽  
Planning Framework ◽  
Planning Algorithm ◽  
Differential Relationship

Motion planning is one of the most important technologies for free-floating space robots (FFSRs) to increase operation safety and autonomy in orbit. As a nonholonomic system, a first-order differential relationship exists between the joint angle and the base attitude of the space robot, which makes it pretty challenging to implement the relevant motion planning. Meanwhile, the existing planning framework must solve inverse kinematics for goal configuration and has the limitation that the goal configuration and the initial configuration may not be in the same connected domain. Thus, faced with these questions, this paper investigates a novel motion planning algorithm based on rapidly-exploring random trees (RRTs) for an FFSR from an initial configuration to a goal end-effector (EE) pose. In a motion planning algorithm designed to deal with differential constraints and restrict base attitude disturbance, two control-based local planners are proposed, respectively, for random configuration guiding growth and goal EE pose-guiding growth of the tree. The former can ensure the effective exploration of the configuration space, and the latter can reduce the possibility of occurrence of singularity while ensuring the fast convergence of the algorithm and no violation of the attitude constraints. Compared with the existing works, it does not require the inverse kinematics to be solved while the planning task is completed and the attitude constraint is preserved. The simulation results verify the effectiveness of the algorithm.

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

2013 ◽  
Vol 16 (04) ◽  
pp. 1350029
Author(s):  
SHIH-FENG HUANG ◽  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
Characteristic Function ◽  
Path Integral ◽  
Unit Root ◽  
Autoregressive Model ◽  
Integral Method ◽  
Unit Root Test ◽  
Random Variable ◽  
Limiting Distribution ◽  
First Order ◽  
Path Integral Method

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

Quenching of Self-Excited Vibrations

1989 ◽  
Vol 111 (2) ◽  
pp. 130-133 ◽  
Author(s):  
K. R. Asfar
Keyword(s):  
Control System ◽  
Vibration Control ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Passive Vibration Control ◽  
First Order ◽  
System A ◽  
Excited System ◽  
Excited Vibration ◽  
First Order Perturbation

A passive vibration control system for the quenching of undesirable self-excited vibrations in mechanical systems is presented. The system is a Lanchester damper, attached to the main self-excited system; a van der Pol oscillator. A first-order perturbation solution shows that complete quenching of self-excited vibration is possible. The result is verified by numerical integration of the governing differential equations. Furthermore, the damper is shown to be effective in suppressing forced self-excited vibrations.

Osmium(VIII) Catalyzed Oxidation of Acetone and Ethylmethyl Ketone by Chloramine-T

1972 ◽  
Vol 27 (10) ◽  
pp. 1161-1163 ◽  
Author(s):  
S. P. Mushran ◽  
R. Sanehi ◽  
M. C. Agraval
Keyword(s):  
Acidic Medium ◽  
Present Note ◽  
Alkaline Media ◽  
Alkaline Solutions ◽  
Slow Step ◽  
First Order ◽  
Chloramine T ◽  
Kinetics Of ◽  
Catalyzed Oxidation ◽  
High Redox Potential

The Osmium (VIII) catalyzed oxidation of acetone and ethylmethyl ketone by chloramine-T, in highly alkaline solutions showed first order dependence to chloramine-T and osmium (VIII). The order of the reactions with respect to alkali and ketone were found to be fractional, being ~-0.82 and 0.3 respectively. No effects of ionic strength were evident. The mechanism has been proposed on the basis of the formation of a complex between N-chlorotoluene-p-sulfonamide and osmium (VIII) in the slow step, which in turn oxidizes the enol anion of the reducing substrate in the fast step.During the study of the mechanism of oxidations by chloramine-T, the kinetics of the oxidation of α-hydroxy acids 1 in presence of osmium (VIII) as catalyst, glycerol2 in neutral and alkaline media, p-cresol3 in an acidic medium, hexacyanoferrate (II)4 in a feebly acidic medium (pH 6-7) and aliphatic aldehydes 5 in alkaline media have been investigated.Despite the high redox potential6 of the chloramine-T/toluene sulfonamide system (1.138 V at pH 12), the oxidation of acetone does not take place in absence of catalyst and that of ethylmethyl ketone proceeds only in highly alkaline solutions7 (NaOH>0.01 M). In the present note the kinetics of the osmium (VIII) catalyzed oxidation of acetone and ethylmethyl ketone have been recorded.

Anisotropic plasma pressure and the dielectric tensor

1970 ◽  
Vol 4 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Tudor Wyatt Johnston
Keyword(s):  
Plasma Pressure ◽  
Dielectric Tensor ◽  
Moment Equations ◽  
Simple Derivation ◽  
Temperature Plasma ◽  
Electrostatic Wave ◽  
Equation Solution ◽  
First Order ◽  
Anisotropic Temperature ◽  
Velocity Moment

The first-order temperature terms for the anisotropic-temperature plasma susceptibility are calculated for each species, using the velocity moment equations and circular polarized co-ordinates. The results agree with the expanded terms for the Vlasov equation solution, for which a usefully simple derivation is given. An electrostatic wave result is given. Drift can be included by a transformation of the results for zero drift.

scholarly journals Tuning and Feasibility Analysis of Classical First-Order MIMO Non-Linear Sliding Mode Control Design for Industrial Applications

Machines ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 10 ◽  
Author(s):  
Alessandro Palmieri ◽  
Renato Procopio ◽  
Andrea Bonfiglio ◽  
Massimo Brignone ◽  
Marco Invernizzi ◽  
...  
Keyword(s):  
Feedback Linearization ◽  
Sliding Mode ◽  
Parameter Tuning ◽  
Industrial Applications ◽  
Single Input Single Output ◽  
First Order ◽  
Control Techniques ◽  
Single Output ◽  
System A ◽  
Single Input

Model-based control techniques have been gaining more and more interest these days. These complex control systems are mostly based on theories, such as feedback linearization, model predictive control, adaptive and robust control. In this paper the latter approach is investigated, in particular, sliding mode (SM) control is analyzed. While several works on the description and application of SM control on single-input single-output systems can easily be found, its application on multi-input multi-output systems is not examined in depth at the same level. Hence, this work aims at formalizing some theoretical complements about the necessary conditions for the feasibility of the SM control for multi-input-multi-output systems. Furthermore, in order to obtain the desired performance from the control system, a method for parameter tuning is proposed in the particular case in which the relative degree of the controlled channels is equal to one. Finally, a simple control problem example is shown with the aim of stressing the benefits derived from the application of the theoretical complements described here.

The Dynamics of a Ball-Type Balancer System Equipped with a Pair of Free-Moving Balancing Masses

2001 ◽  
Vol 123 (4) ◽  
pp. 456-465 ◽  
Author(s):  
Jaan-Rong Kang ◽  
Chang-Po Chao ◽  
Chun-Lung Huang ◽  
Cheng-Kuo Sung
Keyword(s):  
High Speed ◽  
Multiple Scales ◽  
Design Guidelines ◽  
Disk Drives ◽  
Rotating System ◽  
Radial Vibrations ◽  
First Order ◽  
System A ◽  
Autonomous Differential Equations ◽  
Steady State Solutions

This study is devoted to evaluate the performance of a ball-type balancer system that is installed in high-speed optical disk drives. The ball-type balancer system, composed of a circular runway and free-moving balls inside, is designed for reducing radial vibrations induced by the inherent unbalance of the rotating system. A balancer system equipped with a pair of balls is considered in this study for its capability to reach possible near-elimination of radial vibrations as opposed to the serious sizing problem of a single balancing-ball system. A mathematical model is first established to describe the dynamics of the balls and rotor system. Utilizing the method of multiple scales and assuming the smallness of radial vibrations, the system dynamics on the slow time scale is represented by eight first-order autonomous differential equations, which accommodate the radial vibratory motions and ball behaviors. The steady-state solutions of these slow equations are then solved and their stability analyzed to predict settling ball positions. The residual vibrations are computed to evaluate the performance of the balancer system and then the design guidelines are distilled for engineers to design the balancer system.

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