Magnetic Bearing with Radial Magnetized Permanent Magnets

Size: px
Start display at page:

Download "Magnetic Bearing with Radial Magnetized Permanent Magnets"

Transcription

1 Wold Applied Sciences Jounal 23 (4): , 2013 ISSN IDOSI Publications, 2013 DOI: /idosi.wasj Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich Vavilov, Flu Rashitovich Ismagilov and Oksana Alexeevna oikova Ufa State Aviation Technical Univesity, Ufa, Russia Submitted: May 18, 2013; Accepted: Jun 15, 2013; Published: Jun 28, 2013 Abstact: The aticle eveals the elevance of magnetic beaings usage in high-speed electical complexes. Found that the use of high-coecive pemanent magnets in magnetic beaings allows to incease thei stength chaacteistics, eliability and to educe thei weight and size paametes The eseaches esults of the magnetic beaing on pemanent magnets ae given. The scheme fo detemining the magnetic beaings on pemanent magnets magnetic field patten is shown. Magnetic beaings on pemanent magnets pesented as the n-adialy magnetized pemanent magnets that allows to use it not only fo ing magnets magnetic field studies, but fo the secto magnets, which ae widely used as electic machines poles. The accepted assumptions fo detemination mathematical models given. The mathematical tool fo detemination the magnetic beaings on pemanent magnets thee-dimensional magnetic field paametes is developed. The simulation esults ae shown in the gaphs. The compaative analysis of expeimental data and compute modeling is given. The esults ae discussed. Key wods: High-speed electical complex Magnetic beaing Pemanent magnet Hybid magnetic beaing INTRODUCTION To solve this poblem it is necessay: In the moden industy the magnetic beaings find the To develop a mathematical model fo detemining the inceasing application in high-speed electical complexes, MPM magnetic induction at any point in space; because it allows to incease enegy efficiency, to To cay out numeical studies of the developed minimize themal losses and also to incease mathematical model and check its adequacy by envionmental fiendliness of such complexes. The use of compute simulation and expeimental studies. high-coecive pemanent magnets (the PM) in magnetic beaings (M) allows to incease thei stength Decision of Reseach Poblems: The scheme fo chaacteistics, eliability and to educe thei weight and detemining the MPM magnetic field patten is shown in size paametes [1, 2]. Figue 1. MPM pesented as the n-adially magnetized Magnetic beaing eseaches [3, 4] aimed at PM that allows to use it not only fo ing magnets detemining the ai gap stength chaacteistics, as they magnetic field studies, but fo the secto magnets, which ae the key indicatos of M seviceability. So, it is ae widely used as electic machines poles. necessay to detemine the patten distibution of M When developing mathematical model the following magnetic field. In [5] pesented expessions fo calculating assumptions wee accepted: the pemanent magnets magnetic field paametes of ectangula shape. ecause in M the cylindical PM ae pemanent magnets magnetic pemeability is constant used, so the expessions [5] may cause a significant eo. and equal to 1, which is typical fo the magnets fom In [6] the cylindical adial magnetized pemanent magnet NdFe; thee-dimensional magnetic field is consideed, but the the envionment magnetic pemeability is equal to awkwadness of solutions pesented limits its application vacuum magnetic pemeability; in pactice. So it s impotant to develop the mathematical tempeatue conditions ae invaiable thoughout tool that allows to detemine the magnetic beaings on MPM opeational pocess; pemanent magnets (MPM) thee-dimensional magnetic Magnetic field component in the y axis diection is field paametes. zeo because of the symmety. Coesponding Autho: D. Vavilov, Ufa State Aviation Technical Univesity, , Ufa, Kal Max Steet, 12, Republic of ashkotostan, Russia 495

2 Fig. 1: The scheme of the secto pemanent magnet (left) and the MPM (ight) The adial component of the PM magnetic induction The solution of expession (2) was made in the adial component, which, accoding to Coulomb's ule, fo pogam complex Mathcad, the following PM paametes any point in space can be defined as [5]: wee thus used: R 1= 28 mm, R 2= 25 mm, l = 6 mm, = 1 T. ( l 2 x) ( b 2) y ( l 2 x) ( b 2) y These paametes wee chosen due to the fact that they + z = actg + actg + coespond to the paametes used fo calculation in [6]. 4 2 z ( l 2 x) + ( b 2 y) + 2z 2 z ( l 2 x) + 2 y) + 2z The esults ae shown in Figue 2. ( l+ 2 x) ( b 2 y) ( l 2 x) 2 y) + actg + actg (1) The analysis of numeical modeling esults showed 2 z ( l+ 2 x) + ( b 2 y) + 2z 2 z ( l 2 x) + 2 y) + 2z thei convegence with the esults eceived on expessions, pesented in [6], the diffeence does not -PM esidual induction; x, y, z-coodinate point, exceed 2-3%. espectively, whee the magnetic induction is calculated; To detemine the adial component of magnetic field l-pm axial length; qr 1 1 (360 q2) R1-the length of in the MPM ai gap fist calculated the extenal magnetic b = pemanent magnet ach; R1-the adius of PM extenal cicle; q 1, q2-secto aches. The expession (1) does not take into account that the magnets in MPM and in hybid magnetic beaings (HM) have a cylindical shape and theefoe it will cause a significant eo, so it s necessay to take into account the cylindical fom of pemanent magnets. The adial component of magnetic induction at a distance, equal to (Figue 1), taking into account that coodinates of z, y ae cylindical, is defined as: q2 ( l 2 x) ( b 2ycos q) actg z q l x + b y q + z q q1 z = sin ( 2 ) ( 2 cos ) 2 sin ( l 2 x) 2ycos q) + actg + 2zsin q ( l 2 x) ( b 2 y) 2( zsin q) ( l + 2 x) ( b 2ycos q) + actg + 2zsin q ( l + 2 x) + ( b 2ycos q) + 2( zsin q) ( l 2 x) 2ycos q) + actg dq 2zsin q ( l 2 x) + 2ycos q) + 2( zsin q) the coodinate of z defined as. h z = + d 2 (2) induction adial component on the expessions simila to expession (2) then, with application of the magnetic fields supeposition pinciple the numeical calculations wee caied out. The esults ae pesented in figue 3. The analysis of the esults showed that at the minimum ai gap the magnetic induction adial component is minimum. The incease in the ai gap leads to incease in a adial component of a magnetic induction to the maximum value. Futhe incease in the ai gap educes the adial component of the magnetic induction. The maximum of the adial component ai gap induction, at the accepted numeical paametes, made 0,15 T, at a ai gap equal to 2 mm. ecause the adial component of foce is diectly popotional to z, the natue of the foce changes is simila to the natue of the changes in magnetic induction. This phenomenon was noted by the authos in [7]. Conside the axial component of the PM magnetic induction, which can be defined as: x = ln 4 (2 x+ l) + (2 y+ b) + 2 z (2 y + b) (2 x+ l) + (2 y b) + 2 z (2 y b) (2 x l) + (2 y b) + 2 z (2 y b) (2 x l) + (2 y+ b) + 2 z (2 y + b) (3) 496

3 Fig. 2: The change of PM magnetic induction adial component at change of the ai gap size Fig. 4: The dependence of the pemanent magnet magnetic induction axial component fom the ai gap size Fig. 5: The change of the magnetic induction axial Fig. 3: The change of the magnetic induction adial component in the MPM ai gap at change of the component in the MPM ai gap at change of the ai gap size ai gap size The analysis of the modeling esults showed that, The magnetic induction axial component at the similaly magnetic induction adial component, axial distance equal to (Figue 1), taking into account the component inceases with the incease in an ai gap fom cylindical coodinates of z, y is defined as: minimum, to the cetain value, calling theshold value of an ai gap, afte which it stats deceasing. Fo a studied q 2 (2 x+ l) + (2ycos q+ b) + 2( zsin q) (2ycos q+ b) case 2 is the theshold ai gap (0,28 T at the ai gap x = 4 (2 x+ l) + (2ycos q b) + 2( zsin q) (2ycos q b) equal to 2 mm). Impotantly, in the small gap, the gap to q1 (4) the theshold, the axial component of the magnetic (2 x l) + (2ycos q b) + 2( zsin q) (2ycos q b) dq induction of moe than 50-70% adial. In the egion of (2 x l) + (2ycos q+ b) + 2( zsin q) (2ycos q+ b) small ai gap, up to the size of a theshold ai gap, the axial component of a magnetic induction is 50-70% moe than Accoding to expession (4) numeical modeling the adial. So, in aea to theshold value of an ai gap the fo one magnet (Fig. 4) and fo the MPM ai gap pushing out axial foces ae moe than pushing away (Fig. 5) also was caied out. Analysis of the esults adial foces. Thus fo adial MPM axial foces ae showed thei convegence with the esults of [6], which paasitic (in a studied case). Fo checking the developed used a moe complex method. The diffeence does not mathematical expessions and fo confimation of the exceed 2-3%. eceived theoetical conclusions the compute modeling 497

4 Fig. 6: Installation fo PM magnetic field eseaches Fig. 7: Compaative analysis of the expeimental esults, the analytical and simulation of MPM powe chaacteistics in the pogam complex movement elative to the magnet 3. The amount of Ansys and MPM, consisting of two secto magnets movement is contolled by the indicato of hou type expeimental eseaches wee caied out. At compute ICH-8. modeling of thee-dimensional model bounday The Figue 7 shows the expeimental and analytical conditions to Diikhl wee used. When modeling the and compute simulation dependence of magnetic following PM paametes wee used: R1 = 30 mm, R2 = 60 induction adial and axial components on the change of mm, l = 6 mm, = 1,22 T, q1 = 0, q2 = /8. As a esult of the ai gap size/ modeling the values of magnetic field induction axial and 1-magnetic induction axial component: (analytical); 2- adial components wee eceived and wee compaed to magnetic induction axial component: (expeiment); 3- expeimental data and to numeical calculations of magnetic induction axial component: (modeling in Ansys); expessions (2),(4). 4-magnetic induction adial component: (analytical); 5- Expeimental eseaches wee caied out on the magnetic induction adial component: (expeiment); 6- authos' setup (Fig. 6). magnetic induction adial component: (modeling in Pesented in Figue 6 installation includes: 1-holdes, Ansys); in which ae set adial magnetized pemanent magnets 2, 3; the magnetic field measuing instument TPU-05 with a CONCLUSIONS set of feele gauges fo measuing the magnetic field adial and axial components 4; magnetic field measuing The esults analysis showed that the toe-out between instument feele gauge ests on the thust block 5, which analytical and expeimental data doesn't exceed 5% and ensues the accuacy on the coodinates x-axis; thust between the compute simulation and expeimental 2%- block 6 and pushe mechanism 7, poviding the magnet 2 3%. The obtained expeimental data confim theoetical 498

5 conclusions and theefoe, the developed mathematical 6. Swann, M.K., J. Watkins and K.R. onstein, models and esults of thei modeling can be used in Pesent limits of opeation of poduct lubicated and pactice at design of magnetic beaings on pemanent th magnetic beaings in pumps. Poceedings of the 14- magnets and hybid magnetic beaings. intenational Pump Uses Symposium, pp: REFERENCES 7. Ravaund, R., G. Lemaquand and V. Lemaquand, Foce and Stiffness of Passive Magnetic eaings Using Pemanent Magnets. Pat 1: Axial 1. Khayullin, I., F. Ismagilov and V. Vavilov, Magnetization. IEEE Tansctions on Magnetics, Hybid magnetic beaings stength detemination fo 45: 7. high-speed spindles. USATU messenge v., 16: Kasilnikov, A., The calculation of attaction 2. Geasin, A., F. Ismagilov and I. Khayullin, foces in high-coecive pemanent magnets in the Repulsive foce axial component analysis in a edge magnetic clutches and flat magnetic systems // multiing magnetic beaings with the axial diection of Jounal of Mechanical Engineeing. Numbe 6. the magnetization. uild in mechanical engineeing, 9. Ravaund, R., G. Lemaquand and V. Lemaquand, instument, 10: Analytical Calculation of the Magnetic 3. Johan, K., Femeey, Pemanentmagnetische Field Ceated by Pemanent-Magnet Rings. Lage: Jülich Foschungschungszentum Jülich. IEEE Tansctions on Magnetics 44: 8, august. 4. Jansen, R. and E. DiRusso, Passive Magnetic 10. Ismagilov, F., I. Khayullin and V. Vavilov, eaing with Feofluid Stabilization. NASA. NASA Magnetic beaings foce chaacteistics TM detemination, depending on the size of the woking 5. Johnson, D., P. Pillay and M. Malenget, ai gap / / USATU messenge, 16, # 8(53): High speed PM moto with hybid magnetic beaing fo kinetic enegy stoage. Confeence Recod-IAS Annual Meeting (IEEE Industy Applications Society), 1:

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

Problems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968)

Problems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968) Poblems of the nd ntenational Physics Olympiads (Budapest Hungay 968) Péte Vankó nstitute of Physics Budapest Univesity of Technical Engineeing Budapest Hungay Abstact Afte a shot intoduction the poblems

More information

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

SIMULATION OF GAS TURBINES OPERATING IN OFF-DESIGN CONDITION

SIMULATION OF GAS TURBINES OPERATING IN OFF-DESIGN CONDITION SIMULAION OF GAS URBINES OPERAING IN OFF-DESIGN CONDIION Analdo Walte: awalte@fem.unicamp.b Univesity of Campinas Dept. of Enegy DE/FEM/Unicamp P.O. Box 6122 - ZIP code 13083-970 - Bazil Abstact. In many

More information

XIIth PHYSICS (C2, G2, C, G) Solution

XIIth PHYSICS (C2, G2, C, G) Solution XIIth PHYSICS (C, G, C, G) -6- Solution. A 5 W, 0 V bulb and a 00 W, 0 V bulb ae connected in paallel acoss a 0 V line nly 00 watt bulb will fuse nly 5 watt bulb will fuse Both bulbs will fuse None of

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

Progress In Electromagnetics Research Letters, Vol. 11, , 2009

Progress In Electromagnetics Research Letters, Vol. 11, , 2009 Pogess In Electomagnetics Reseach Lettes, Vol. 11, 93 102, 2009 COMPUTATIONAL MODELING OF INDUCTION HEATING PROCESS M. H. Tavakoli, H. Kabaschi, and F. Samavat Physics Depatment Bu-Ali Sina Univesity Hamedan

More information

MATHEMATICAL SIMULATION OF MASS SPECTRUM

MATHEMATICAL SIMULATION OF MASS SPECTRUM MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec

More information

Channel selection in e-commerce age: A strategic analysis of co-op advertising models

Channel selection in e-commerce age: A strategic analysis of co-op advertising models Jounal of Industial Engineeing and Management JIEM, 013 6(1):89-103 Online ISSN: 013-0953 Pint ISSN: 013-843 http://dx.doi.og/10.396/jiem.664 Channel selection in e-commece age: A stategic analysis of

More information

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation

Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation Cicuits and Systems, 013, 4, 117-1 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0

More information

Study on In-situ Capacitive Sensor for Monitoring Engine Lubricant Oil Debris

Study on In-situ Capacitive Sensor for Monitoring Engine Lubricant Oil Debris 8th Euopean Wokshop On Stuctual Health Monitoing (EWSHM 016), 5-8 July 016, Spain, Bilbao www.ndt.net/app.ewshm016 Study on In-situ Capacitive Senso fo Monitoing Engine Lubicant Oil Debis Moe info about

More information

Software Engineering and Development

Software Engineering and Development I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining

More information

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

More information

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE 1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of

More information

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS

ON THE (Q, R) POLICY IN PRODUCTION-INVENTORY SYSTEMS ON THE R POLICY IN PRODUCTION-INVENTORY SYSTEMS Saifallah Benjaafa and Joon-Seok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poduction-inventoy

More information

Modelling and Simulation of Four Quadrant Operation of Three Phase Brushless DC Motor With Hysteresis Current Controller

Modelling and Simulation of Four Quadrant Operation of Three Phase Brushless DC Motor With Hysteresis Current Controller ISSN (Pint) : 30 375 Vol., Issue, June 03 Modelling and Simulation of Fou Quadant Opeation of Thee Phase Bushless DC Moto With Hysteesis Cuent Contolle Sanita C S, J T Kuncheia PG Student [IDAC], Dept.

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds. Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of

More information

STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION

STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium

More information

Chapter 6. Gradually-Varied Flow in Open Channels

Chapter 6. Gradually-Varied Flow in Open Channels Chapte 6 Gadually-Vaied Flow in Open Channels 6.. Intoduction A stea non-unifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gadually-vaied flow (GVF). The backwate

More information

Research on Risk Assessment of the Transformer Based on Life Cycle Cost

Research on Risk Assessment of the Transformer Based on Life Cycle Cost ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow

More information

8-1 Newton s Law of Universal Gravitation

8-1 Newton s Law of Universal Gravitation 8-1 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

Lab #7: Energy Conservation

Lab #7: Energy Conservation Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 1-4 Intoduction: Pehaps one of the most unusual

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

More information

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado

More information

Carter-Penrose diagrams and black holes

Carter-Penrose diagrams and black holes Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example

More information

Section 5-3 Angles and Their Measure

Section 5-3 Angles and Their Measure 5 5 TRIGONOMETRIC FUNCTIONS Section 5- Angles and Thei Measue Angles Degees and Radian Measue Fom Degees to Radians and Vice Vesa In this section, we intoduce the idea of angle and two measues of angles,

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

More information

4.1 Cylindrical and Polar Coordinates

4.1 Cylindrical and Polar Coordinates 4.1 Cylindical and Pola Coodinates 4.1.1 Geometical Axisymmety A lage numbe of pactical engineeing poblems involve geometical featues which have a natual axis of symmety, such as the solid cylinde, shown

More information

Problems of the 2 nd and 9 th International Physics Olympiads (Budapest, Hungary, 1968 and 1976)

Problems of the 2 nd and 9 th International Physics Olympiads (Budapest, Hungary, 1968 and 1976) Poblems of the nd and 9 th Intenational Physics Olympiads (Budapest Hungay 968 and 976) Péte Vankó Institute of Physics Budapest Univesity of Technology and Economics Budapest Hungay Abstact Afte a shot

More information

NUCLEAR MAGNETIC RESONANCE

NUCLEAR MAGNETIC RESONANCE 19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

Gauss Law in dielectrics

Gauss Law in dielectrics Gauss Law in dielectics We fist deive the diffeential fom of Gauss s law in the pesence of a dielectic. Recall, the diffeential fom of Gauss Law is This law is always tue. E In the pesence of dielectics,

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuent-caying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to

More information

Problem Set 6: Solutions

Problem Set 6: Solutions UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

More information

Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud

Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The

More information

Physics 202, Lecture 4. Gauss s Law: Review

Physics 202, Lecture 4. Gauss s Law: Review Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25-Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential

More information

New proofs for the perimeter and area of a circle

New proofs for the perimeter and area of a circle New poofs fo the peimete and aea of a cicle K. Raghul Kuma Reseach Schola, Depatment of Physics, Nallamuthu Gounde Mahalingam College, Pollachi, Tamil Nadu 64001, India 1 aghul_physics@yahoo.com aghulkumak5@gmail.com

More information

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :(

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :( You Comments Llamas, and why it is so difficult to get someone to buy me one as a pet. All ask is that it beathes fie. have simple needs people. Seiously. p.s. this lectue was had. did not undestand any

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

Forces & Magnetic Dipoles. r r τ = μ B r

Forces & Magnetic Dipoles. r r τ = μ B r Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent

More information

The Critical Angle and Percent Efficiency of Parabolic Solar Cookers

The Critical Angle and Percent Efficiency of Parabolic Solar Cookers The Citical Angle and Pecent Eiciency o Paabolic Sola Cookes Aiel Chen Abstact: The paabola is commonly used as the cuve o sola cookes because o its ability to elect incoming light with an incoming angle

More information

The Doppler Effect in Warning Signals: Perceptual Investigations into Aversive Reactions Related to Pitch Changes

The Doppler Effect in Warning Signals: Perceptual Investigations into Aversive Reactions Related to Pitch Changes The Dopple Effect in Waning Signals: Peceptual Investigations into Avesive Reactions Related to Pitch Changes Clemens Kuhn-Rahloff & Matin Neukom Institute fo Compute Music and Sound Technology (ICST,

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,

More information

Heat transfer has direction as well as magnitude. The rate of heat conduction

Heat transfer has direction as well as magnitude. The rate of heat conduction HEAT CONDUCTION EQUATION CHAPTER 2 Heat tansfe has diection as well as magnitude. The ate of heat conduction in a specified diection is popotional to the tempeatue gadient, which is the ate of change in

More information

EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN- ROOF OF A CAR

EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN- ROOF OF A CAR EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN- ROOF OF A CAR Liang S. Lai* 1, Geogi S. Djambazov 1, Choi -H. Lai 1, Koulis A. Peicleous 1, and Fédéic Magoulès

More information

LAL Update. Letter From the President. Dear LAL User:

LAL Update. Letter From the President. Dear LAL User: LAL Update ASSOCIATES OF CAPE COD, INCORPORATED OCTOBER 00 VOLUME 0, NO. Lette Fom the Pesident Dea LAL Use: This Update will claify some of the statistics used with tubidimetic and chomogenic LAL tests.

More information

OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS

OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS Ronald De Fou Depatment of Electical & Compute Engineeing, The Univesity of the West Indies St. Augustine, Tinidad defou@eng.uwi.tt Emily Ramouta Univesity

More information

Mon., 3/9 Tues., 3/10 Wed., 3/11 Thurs., 3/12 Fri., 3/ 13. RE19 HW19:RQ.42, 49, 52; P.61, 66, 69 RE20, Exp new RE ,3-4 Magnetic Force

Mon., 3/9 Tues., 3/10 Wed., 3/11 Thurs., 3/12 Fri., 3/ 13. RE19 HW19:RQ.42, 49, 52; P.61, 66, 69 RE20, Exp new RE ,3-4 Magnetic Force Mon., 3/9 Tues., 3/10 Wed., 3/11 Thus., 3/12 Fi., 3/ 13 Mon., 3/16 Tues., 3/17 Wed., 3/18 Thus., 3/19 Fi., 3/20 20.1,3-4 Magnetic Foce 20.2,5 Cuent and Motional Emf Quiz Ch 19, Lab 8 Cycloton & Electon

More information

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications JIS (Japanese Industial Standad) Scew Thead Specifications TECNICAL DATA Note: Although these specifications ae based on JIS they also apply to and DIN s. Some comments added by Mayland Metics Coutesy

More information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

More information

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions Name St.No. - Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100-minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

Fluids Lecture 15 Notes

Fluids Lecture 15 Notes Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2-D, this velocit

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

Modal Characteristics study of CEM-1 Single-Layer Printed Circuit Board Using Experimental Modal Analysis

Modal Characteristics study of CEM-1 Single-Layer Printed Circuit Board Using Experimental Modal Analysis Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM-1 Single-Laye

More information

Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy

Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy Intenational Jounal of Poduction Reseach ISSN: -753 Pint 1366-588X Online Jounal homepage: http://www.tandfonline.com/loi/tps Dual channel closed-loop supply chain coodination with a ewad-diven emanufactuing

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

Reduced Pattern Training Based on Task Decomposition Using Pattern Distributor

Reduced Pattern Training Based on Task Decomposition Using Pattern Distributor > PNN05-P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto Sheng-Uei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task

More information

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING

HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING U.P.B. Sci. Bull., Seies C, Vol. 77, Iss. 2, 2015 ISSN 2286-3540 HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING Roxana MARCU 1, Dan POPESCU 2, Iulian DANILĂ 3 A high numbe of infomation systems ae available

More information

Nuclear models: Fermi-Gas Model Shell Model

Nuclear models: Fermi-Gas Model Shell Model Lectue Nuclea mode: Femi-Gas Model Shell Model WS/: Intoduction to Nuclea and Paticle Physics The basic concept of the Femi-gas model The theoetical concept of a Femi-gas may be applied fo systems of weakly

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

1.4 Phase Line and Bifurcation Diag

1.4 Phase Line and Bifurcation Diag Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

USB True Emulation for KVM Switches. Transparent and reliable USB KVM switching technology.

USB True Emulation for KVM Switches. Transparent and reliable USB KVM switching technology. Tanspaent and eliable KVM switching technology. 0118 724-746-5500 965 6000 www.blackbox.co.uk blackbox.com Table of Contents Intoduction... 3 Enumeated Switching... 4 Emulated Switching... 5 Tue Emulation...

More information

THERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS

THERMAL ISOLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS THERMAL OLATION TECHNIQUES FOR CURE MONITORING USING FBG OPTICAL SENSORS E.K.G. Boateng, P.J. Schubel, N.A. Waio Polyme Composites Goup Division of Mateials, Mechanics and Stuctues Faculty of Engineeing

More information

High Availability Replication Strategy for Deduplication Storage System

High Availability Replication Strategy for Deduplication Storage System Zhengda Zhou, Jingli Zhou College of Compute Science and Technology, Huazhong Univesity of Science and Technology, *, zhouzd@smail.hust.edu.cn jlzhou@mail.hust.edu.cn Abstact As the amount of digital data

More information

2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90

2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90 . Tigonometic Ratios of An Angle Focus on... detemining the distance fom the oigin to a point (, ) on the teminal am of an angle detemining the value of sin, cos, o tan given an point (, ) on the teminal

More information

Smart Antenna Array Calibration Procedure Including Amplitude and Phase Mismatch and Mutual Coupling Effects

Smart Antenna Array Calibration Procedure Including Amplitude and Phase Mismatch and Mutual Coupling Effects Smat Antenna Aay alibation Pocedue Including Amplitude and Phase Mismatch and Mutual oupling Effects Kapil R. Dandeka, Hao Ling, and Guanghan Xu Univesity of Texas at Austin, Dept. of Elec. And omp. Eng.

More information

Trigonometric Functions of Any Angle

Trigonometric Functions of Any Angle Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An

More information

AP Physics Electromagnetic Wrap Up

AP Physics Electromagnetic Wrap Up AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle

More information

An Introduction to Omega

An Introduction to Omega An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Today in Physics 217: multipole expansion

Today in Physics 217: multipole expansion Today in Physics 17: multipole expansion Multipole expansions Electic multipoles and thei moments Monopole and dipole, in detail Quadupole, octupole, Example use of multipole expansion as appoximate solution

More information

Lesson 7 Gauss s Law and Electric Fields

Lesson 7 Gauss s Law and Electric Fields Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual

More information

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This

More information

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea Double Integals in Pola Coodinates In the lectue on double integals ove non-ectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example

More information

L19 Geomagnetic Field Part I

L19 Geomagnetic Field Part I Intoduction to Geophysics L19-1 L19 Geomagnetic Field Pat I 1. Intoduction We now stat the last majo topic o this class which is magnetic ields and measuing the magnetic popeties o mateials. As a way o

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information