GEOID-QUASIGEOID CORRECTION IN FORMULATION OF THE FUNDAMENTAL FORMULA OF PHYSICAL GEODESY. Robert Tenzer 1 Petr Vaníček 2
|
|
- Jocelyn Lang
- 6 years ago
- Views:
Transcription
1 GEID-QUASIGEID CECTI I FMULATI F TE FUDAMETAL FMULA F PYSICAL GEDESY be Tenze 1 Pe Vaníček 1 Depamen f Gedesy and Gemaics Enineein Univesiy f ew Bunswick P Bx 4400 Fedeicn ew Bunswick Canada E3B 5A3; Tel enze@unbca Depamen f Gedesy and Gemaics Enineein Univesiy f ew Bunswick P Bx 4400 Fedeicn ew Bunswick Canada E3B 5A3; Tel vanicek@unbca ABSTACT T fmulae he fundamenal fmula f physical edesy a he physical suface f he Eah he aviy anmalies ae used insead f he aviy disubances because he edeic heihs abve he ecenic efeence ellipsid ae n usually available The elain beween he aviy anmaly and he aviy disubance is defined as a pduc f he nmal aviy adien efeed he elluid and he heih anmaly accdin Mldensky s hey f he nmal heihs (Mldensky 1945; Mldensky e al 1960) Cnsidein he nmal aviy adien efeed he suface f he ecenic efeence ellipsid his elain is edefined as a funcin f he nmal heih (Vaníček e al 1999) When he hmeic heihs ae pacically used f he ealizain f he veical daum he eid-quasieid cecin is applied he fundamenal fmula f physical edesy deemine he pecise eid Theeical fmulain f he eid-quasieid cecin he fundamenal fmula f physical edesy can be fund in Mainec (1993) and Vaníček e al (1999) In his pape he numeical invesiain f his cecin a he eiy f Canada is shwn and he e analysis is induced Keywds Geid-Quasieid Cecin aviy heih 1 BASIC TEY The aviy disubance [ he Eah s suface δ efeed whee denes he ecenic adius f he eid suface is defined by (eiskanen and Miz 1967 Eq -146) δ [ = [ [ γ (1) whee ) is he acual aviy and γ ( is he nmal aviy f he ecenic efeence ellipsid The nmal aviy is defined accdin Smiliana Pizzei s hey f he nmal aviy field eneaed by he ellipsid f evluin (Pizzei 1894 and 1911; Smiliana 199) A ecenic psiin is epesened by he ecenic adius ; 0 ) and he ecenic spheical cdinaes φ and λ ; = ( φ λ) ( π/ π/; 0 λ π ) [ φ Since he evaluain f he nmal aviy γ a he Eah s suface wuld equie he knwlede f he edeic heih h abve he ecenic efeence ellipsid he aviy disubance δ [ is ansfmed in he aviy anmaly [ accdin he fllwin equain (Vaníček e al 1999) [ δ [ γ [ γ ( = = () In Eq () denes he nmal heih ( γ is he nmal aviy efeed he suface f he ecen- φ π / π / φ and ic efeence ellipsid ( / is he nmal aviy adien GEID-QUASIGEID CECTI When he hmeic heihs insead f he nmal heihs ae used he eidquasieid cecin is applied Eq () T define his cecin he cmmnly used elme s hme- evisa Basileia de Caafia º 55/01
2 ic heihs and Mldensky s nmal heihs ae biefly induced The fundamenal fmula f a definiin f he hmeic heih eads (eiskanen and Miz 1967) C [ = (3) whee C [ is he epenial numbe and is he mean value f he aviy aln he plumbline beween he eid and he Eah s suface F he elme (1890) hmeic heih he mean value f he aviy is evaluaed usin Pincaé-Pey s aviy adien (eiskanen and Miz 1967 Eq 4-5) [ 1 ) = ( ) [ = π G ρ (4) is he bseved aviy a he Eah s whee [ suface G is ewn s aviainal cnsan and ρ 3 is he mean paphical densiy ρ = 67 [ cm Mldensky s nmal heih eads (Mldensky 1945) C [ = (5) γ The mean value f he nmal aviy γ aln he ellipsidal nmal beween he suface f he ecenic efeence ellipsid and he elluid φ is iven by γ γ [ ( 4 = [ = φ ( ) (6) The diffeence beween he nmal heih and hmeic heih ie he eid-quasieid cecin can be fund beinnin wih he fllwin elain γ = γ Assumin γ 4 γ γ ( (7) [ (8) he diffeence beween he mean aviy and he mean nmal aviy γ in Eq (7) becmes γ [ γ [ ( (9) πg ρ The expessin n he ih-hand side f Eq (9) is appximaely equal he simple Buue aviy anmaly [ (Mainec 1993) [ [ = γ φ = πg ρ (10) eadin Eq (10) he eid-quasieid cecin fm Eq (7) finally akes he fllwin fm [ γ ( (11) Subsiuin Eq (11) Eq () he aviy anmaly [ becmes = δ γ γ φ [ [ [ γ 1 = [ γ ( [ whee [ sands f he fee-ai aviy anmaly [ = [ ( = γ φ φ 1 γ = [ (1) γ (13) Applyin he spheical appximain (eiskanen and Miz 1967 Eq -150) 1 (14) γ φ ( Eq (1) is subsequenly ewien as [ = [ [ (15) The secnd em n he ih-hand side f Eq (15) defines he eid-quasieid cecin he fundamenal fmula f physical edesy (Vaníček e al 1999) [ [ (16) evisa Basileia de Caafia º 55 58
3 3 E AALYSIS The accuacy esimain f he eidquasieid cecin [ he fundamenal fmula f physical edesy depends n he accuacy f he hmeic heih aviy and paphical densiy Fm Eq (16) fllws he elain beween he acual e [ f he eid-quasieid cecin he fundamenal fmula f physical edesy and he e f he hmeic heih and he e [ f he simple Buue aviy anmaly [ [ [ = [ [ = [ [ [ = [ [ (17) Fuheme he e [ f he simple Buue aviy anmaly is expessed by [ [ = [ [ ( ) [ [ γ φ γ [ ( [ δρ ρ [ [ [ [ [ δρ ρ whee [ [ (18) is he acual e f he bseved aviy a he Eah s suface The laeally vayin anma- δρ is iven by a diffe- lus paphical densiy ence f he laeal paphical densiy ρ and he mean paphical densiy ρ (Mainec 1993) δρ = ρ ρ (19) The e f he cecin [ caused by he inaccuacy f he nmal aviy γ [ ( due he e ( ) f he hmeic heih is neliible [ [ [ φ φ = [ [ γ ( = ω a b γ ( 1 f f sin φ a GM (0) Theefe he e [ f he bseved aviy is pacically equivalen he e f he fee-ai aviy anmaly [ s ha [ [ In Eq (0) a b ae he semi-axes and f is he fis numeical flaenin f he ecenic efeence ellipsid ω is he mean anula velciy f he Eah s spin and GM sands f he ecenic aviainal cnsan Pefmin he paial deivaives f he simple Buue aviy anmaly [ wih espec he hmeic heih and aviy [ paphical densiy ρ Eq (18) akes he fllwin fm [ = [ π G ρ ( ) π G δρ( ) (1) Subsiuin Eq (1) Eq (17) he al diffeenial hlds [ [ [ [ = [ [ [ δρ( ) ρ [ [ [ [ [ [ 4π G ρ [ 4π G = δρ 4 UMEICAL IVESTIGATI [ () The eid-quasieid cecin [ he fundamenal fmula f physical edesy is a linea funcin f he fee-ai aviy anmaly [ and paphical densiy hmeic heih ρ insead f he mean paphical densiy ρ nly The elain beween he cecin [ and he fee-ai aviy anmaly is shwn in Fi 1 evisa Basileia de Caafia º 55 59
4 Fiue 1- elain beween he eid-quasieid c- [ he fundamenal fmula f physical ecin edesy and he fee-ai aviy anmalies [ 3 (wae) 98 [ cm The e = 100 [m f he hmeic heih causes he inaccuacy 4 [µgal f he eidquasieid cecin [ he fundamenal fmula f physical edesy f he heih 6000 [m (Fi ) The eal paphical densiy ρ vaies fm 10 (abb) When he eal densiy f he paphical masses is cnsideed diseadin exisin wae bdies he vaiain f densiy is appximaely wihin he ineval 3 δρ cm aund he mean value [ ρ The vaiain f he paphical densiy δρ can cause hunded f micals e f he eidquasieid cecin he bunday value pblem (Fi 4) n he he hand he inaccuacy f his cecin due he e [ f he fee-ai aviy anmalies is nly a few micals (Fi 3) Fiue 4- E [ f he eid-quasieid cecin he fundamenal fmula f physical edesy due he vaiain f he paphical densiy δρ ρ The eid-quasieid cecin [ he fundamenal fmula f physical edesy has been cmpued a he eiy f Canada (Fi 5) A his eiy i vaies fm [mgal wih he mean value equal 0013 [mgal The maniude f he celain beween his cecin and he vaiain f he laeal paphical densiy δρ is beween 0036 and 003 [mgal see Fi 6 Fiue 5- The eid-quasieid cecin [ he fundamenal fmula f physical edesy a he eiy f Canada [mgal Fiue - elain beween he e f he eid- he fundamenal quasieid cecin [ fmula f physical edesy and he e f he hmeic heih [ Fiue 6- Vaiain f he eid-quasieid cecin he fundamenal fmula f physical edesy wih laeal paphical densiy δρ -8 [µgal = 10 ms Fiue 3- elain beween he e f he eid- he fundamenal quasieid cecin [ fmula f physical edesy and he e [ he fee-ai aviy anmaly f 5 CCLUSI T incease he accuacy f he eidquasieid cecin he laeally vayin paphical densiy can be used f he cmpuain f he simple Buue aviy anmaly Accdin he e ppaain in Chape 3 he chane f he paphical densiy causes he laes e f he eidquasieid cecin he fundamenal fmula f physical edesy Fm he numeical esul ve he eiy f Canada fllws ha he vaiain f his cecin due he anmalus paphical densiy is up ± 40 micals evisa Basileia de Caafia º 55 60
5 6 EFEECES EISKAE WA MITZ 1967 Physical edesy W Feeman and C San Fancisc ELMET F 1890 Die Schwekaf im chebie insbesndee in den Tyle Alpen Veöff Könil Peuss Ged Ins Vl 1 MATIEC Z 1993 Effec f laeal densiy vaiains f paphical masses in view f impvin eid mdel accuacy ve Canada Final ep f cnac DSS Gedeic Suvey f Canada awa MLDESKY MS 1945 Fundamenal pblems f Gedeic Gavimey (in ussian) TUDY Ts IIGAIK 4 Gedezizda Mscw MLDESKY MS YEEMEEV VF YUK- IA MI 1960 Mehds f Sudy f he Exenal Gaviainal Field and Fiue f he Eah TUDY Ts IIGAiK 131 Gedezizda Mscw Enlish ansla Isael Pam f Scienific Tanslain Jeusalem 196 PIZZETTI P 1894 Sulla espessine della avià alla supeficie del eide supps ellissidic Ai Accad Lincei se V V3 PIZZETTI P 1911 Spa il calcl eic delle deviazini del eide dall` ellisside Ai Accad Sci Tin V 46 SMIGLIAA C 199 Teia Geneale del Camp Gaviazinale dell Elliside di azine Memie della Sciea Asnmica Ialiana IV Milan VAÍČEK P UAG J VÁK P PAGIATAKIS SD VÉEAU M MA- TIEC Z FEATESTE WE 1999 Deeminain f he bunday values f he Skes- elme pblem Junal f Gedesy Vl 73 Spine pp evisa Basileia de Caafia º 55 61
MEAN GRAVITY ALONG PLUMBLINE. University of New Brunswick, Department of Geodesy and Geomatics Engineering, Fredericton, N.B.
MEA GRAVITY ALG PLUMBLIE Beh-Anne Main 1, Chis MacPhee, Rbe Tenze 1, Pe Vaníek 1 and Macel Sans 1 1. Inducin 1 Univesiy f ew Bunswick, Depamen f Gedesy and Gemaics Engineeing, Fedeicn,.B., E3B 5A3, Canada
More information11. HAFAT İş-Enerji Power of a force: Power in the ability of a force to do work
MÜHENDİSLİK MEKNİĞİ. HFT İş-Eneji Pwe f a fce: Pwe in he abiliy f a fce d wk F: The fce applied n paicle Q P = F v = Fv cs( θ ) F Q v θ Pah f Q v: The velciy f Q ÖRNEK: İŞ-ENERJİ ω µ k v Calculae he pwe
More informationOn Some Numerical Aspects of Primary Indirect Topographical Effect Computation in the Stokes-Helmert Theory of Geoid Determination
n Some Numeical Aspecs of Pimay Indiec Topoaphical Effec Compuaion in he Sokes-Helme Theoy of Geoid Deeminaion obe Tenze Pe Vaníek Sande van Eck van de Sluijs Anonio Henández-Navao 4 Absac Afe solvin he
More informationPart 2 KINEMATICS Motion in One and Two Dimensions Projectile Motion Circular Motion Kinematics Problems
Pa 2 KINEMATICS Min in One and Tw Dimensins Pjecile Min Cicula Min Kinemaics Pblems KINEMATICS The Descipin f Min Physics is much me han jus he descipin f min. Bu being able descibe he min f an bjec mahemaically
More information2. The units in which the rate of a chemical reaction in solution is measured are (could be); 4rate. sec L.sec
Kineic Pblem Fm Ramnd F. X. Williams. Accding he equain, NO(g + B (g NOB(g In a ceain eacin miue he ae f fmain f NOB(g was fund be 4.50 0-4 ml L - s -. Wha is he ae f cnsumpin f B (g, als in ml L - s -?
More informationTransient Radial Flow Toward a Well Aquifer Equation, based on assumptions becomes a 1D PDE for h(r,t) : Transient Radial Flow Toward a Well
ansien Radial Flw wad a Well Aqife Eqain, based n assmpins becmes a D PDE f h(,) : -ansien flw in a hmgenes, ispic aqife -flly peneaing pmping well & infinie, hiznal, cnfined aqife f nifm hickness, hs
More informationOn Some Aspects of Accuracy of the Geopotential Model EMG96 at the Territory of Canada
n Sme Aspecs f Accuracy f he Gepenial Mdel EMG96 a he Terriry f Canada Rber Tenzer 1 Anni Hernández-avarr Absrac The gepenial mdel esing mehdlgy has been hereically develped by Burke e al. [1996. The Wrking
More informationCircular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can.
1 Cicula Moion Radians One evoluion is equivalen o 360 0 which is also equivalen o 2π adians. Theefoe we can say ha 360 = 2π adians, 180 = π adians, 90 = π 2 adians. Hence 1 adian = 360 2π Convesions Rule
More informationAutomatic Measuring of English Language Proficiency using MT Evaluation Technology
Aumaic Measuing f English Language Pficiency using MT Evaluain Technlgy Keiji Yasuda ATR Spken Language Tanslain Reseach Labaies Depamen f SLR 2-2-2 Hikaidai, Keihanna Science Ciy Ky 69-0288 Japan keiji.yasuda@a.jp
More informationGeneral Non-Arbitrage Model. I. Partial Differential Equation for Pricing A. Traded Underlying Security
1 Geneal Non-Abiage Model I. Paial Diffeenial Equaion fo Picing A. aded Undelying Secuiy 1. Dynamics of he Asse Given by: a. ds = µ (S, )d + σ (S, )dz b. he asse can be eihe a sock, o a cuency, an index,
More informationExample
hapte Exaple.6-3. ---------------------------------------------------------------------------------- 5 A single hllw fibe is placed within a vey lage glass tube. he hllw fibe is 0 c in length and has a
More informationMaxwell Equations. Dr. Ray Kwok sjsu
Maxwell quains. Ray Kwk sjsu eeence: lecmagneic Fields and Waves, Lain & Csn (Feeman) Inducin lecdynamics,.. Giihs (Penice Hall) Fundamenals ngineeing lecmagneics,.k. Cheng (Addisn Wesley) Maxwell quains.
More informationWYSE Academic Challenge Sectional Mathematics 2006 Solution Set
WYSE Academic Challenge Sectinal 006 Slutin Set. Cect answe: e. mph is 76 feet pe minute, and 4 mph is 35 feet pe minute. The tip up the hill takes 600/76, 3.4 minutes, and the tip dwn takes 600/35,.70
More informationOBJECTIVE To investigate the parallel connection of R, L, and C. 1 Electricity & Electronics Constructor EEC470
Assignment 7 Paallel Resnance OBJECTIVE T investigate the paallel cnnectin f R,, and C. EQUIPMENT REQUIRED Qty Appaatus 1 Electicity & Electnics Cnstuct EEC470 1 Basic Electicity and Electnics Kit EEC471-1
More informationDesign Guideline for Buried Hume Pipe Subject to Coupling Forces
Design Guideline fo Buied Hume Pipe Sujec o Coupling Foces Won Pyo Hong 1), *Seongwon Hong 2), and Thomas Kang 3) 1) Depamen of Civil, nvionmenal and Plan ngineeing, Chang-Ang Univesiy, Seoul 06974, Koea
More informationHeat transfer between shell and rigid body through the thin heat-conducting layer taking into account mechanical contact
Advanced Cmpuainal Meds in Hea Tansfe X 8 Hea ansfe beween sell and igid bdy ug e in ea-cnducing laye aking in accun mecanical cnac V. V. Zzulya Cen de Invesigación Cienífica de Yucaán, Méida, Yucaán,
More informationSolution of a Spherically Symmetric Static Problem of General Relativity for an Elastic Solid Sphere
Applied Physics eseach; Vol. 9, No. 6; 7 ISSN 96-969 E-ISSN 96-9647 Published by Canadian Cente of Science and Education Solution of a Spheically Symmetic Static Poblem of Geneal elativity fo an Elastic
More informationVisco-elastic Layers
Visc-elasic Layers Visc-elasic Sluins Sluins are bained by elasic viscelasic crrespndence principle by applying laplace ransfrm remve he ime variable Tw mehds f characerising viscelasic maerials: Mechanical
More informationMaximum Cross Section Reduction Ratio of Billet in a Single Wire Forming Pass Based on Unified Strength Theory. Xiaowei Li1,2, a
Inenainal Fum n Enegy, Envinmen and Susainable evelpmen (IFEES 06 Maximum Css Sein Reduin Rai f Bille in a Single Wie Fming Pass Based n Unified Sengh They Xiawei Li,, a Shl f Civil Engineeing, Panzhihua
More informationComputer Propagation Analysis Tools
Compue Popagaion Analysis Tools. Compue Popagaion Analysis Tools Inoducion By now you ae pobably geing he idea ha pedicing eceived signal sengh is a eally impoan as in he design of a wieless communicaion
More informationME 3600 Control Systems Frequency Domain Analysis
ME 3600 Cntl Systems Fequency Dmain Analysis The fequency espnse f a system is defined as the steady-state espnse f the system t a sinusidal (hamnic) input. F linea systems, the esulting utput is itself
More informationWork, Energy, and Power. AP Physics C
k, Eneg, and Pwe AP Phsics C Thee ae man diffeent TYPES f Eneg. Eneg is expessed in JOULES (J) 4.19 J = 1 calie Eneg can be expessed me specificall b using the tem ORK() k = The Scala Dt Pduct between
More informationThe Flatness Problem as A Natural Cosmological Phenomenon
Inenainal Junal f Pue and Applied Physics ISSN 0973-1776 Vlume 4, Numbe (008), pp. 161 169 Reseach India Publicains hp://www.ipublicain.cm/ijpap.hm The Flaness Pblem as A Naual Csmlgical Phenmenn 1 Maumba
More informationJournal of Theoretics
Junal f Theetics Junal Hme Page The Classical Pblem f a Bdy Falling in a Tube Thugh the Cente f the Eath in the Dynamic They f Gavity Iannis Iaklis Haanas Yk Univesity Depatment f Physics and Astnmy A
More informationLecture 18: Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation
Lecue 8: Kineics of Phase Gowh in a Two-componen Sysem: geneal kineics analysis based on he dilue-soluion appoximaion Today s opics: In he las Lecues, we leaned hee diffeen ways o descibe he diffusion
More information, on the power of the transmitter P t fed to it, and on the distance R between the antenna and the observation point as. r r t
Lecue 6: Fiis Tansmission Equaion and Rada Range Equaion (Fiis equaion. Maximum ange of a wieless link. Rada coss secion. Rada equaion. Maximum ange of a ada. 1. Fiis ansmission equaion Fiis ansmission
More informationApplication of Fractional Calculus in Food Rheology E. Vozáry, Gy. Csima, L. Csapó, F. Mohos
Applicain f Facinal Calculus in F Rhelgy Szen Isán Uniesiy, Depamen f Physics an Cnl Vzay.sze@ek.szie.hu Keyws: facinal calculus, iscelasic, f, ceep, ecey Absac. In facinal calculus he e (β) f iffeeniain
More informationConsider the simple circuit of Figure 1 in which a load impedance of r is connected to a voltage source. The no load voltage of r
1 Intductin t Pe Unit Calculatins Cnside the simple cicuit f Figue 1 in which a lad impedance f L 60 + j70 Ω 9. 49 Ω is cnnected t a vltage suce. The n lad vltage f the suce is E 1000 0. The intenal esistance
More information( ) ( ) CHAPTER 8. Lai et al, Introduction to Continuum Mechanics. Copyright 2010, Elsevier Inc 8-1
CHAPER 8 81 Shw ha f an incmpessible Newnian fluid in Cuee flw he pessue a he ue cylinde ( R ) is always lage han ha a he inne cylinde ha is bain R i Ri ρ ω R R d B Ans In Cuee flw v vz and vθ A+ [see
More informationROLE OF NO TOPOGRAPHY SPACE IN STOKES-HELMERT SCHEME FOR GEOID DETERMINATION
LE F N TPGAPY SPACE IN STKES-ELMET SCEME F GEID DETEMINATIN Per Vaníek, ober Tenzer and Jianliang uang Annual meeing of CGU 1 We have been formalizing he Sokes soluion of he geodeic boundary value problem
More informationCHAPTER GAUSS'S LAW
lutins--ch 14 (Gauss's Law CHAPTE 14 -- GAU' LAW 141 This pblem is ticky An electic field line that flws int, then ut f the cap (see Figue I pduces a negative flux when enteing and an equal psitive flux
More informationChapter 4 Motion in Two and Three Dimensions
Chapte 4 Mtin in Tw and Thee Dimensins In this chapte we will cntinue t stud the mtin f bjects withut the estictin we put in chapte t me aln a staiht line. Instead we will cnside mtin in a plane (tw dimensinal
More informationLecture 22 Electromagnetic Waves
Lecue Elecomagneic Waves Pogam: 1. Enegy caied by he wave (Poyning veco).. Maxwell s equaions and Bounday condiions a inefaces. 3. Maeials boundaies: eflecion and efacion. Snell s Law. Quesions you should
More informationMilos Pick Geophysical Institute of the Czech Academy of Sciences, Czech Republic.
GRAVIMETRY Mils Pick Gephysical Institute f the Czech Academy f Sciences, Czech Republic. Keywds:Gavimety, gavity ptential, gavity fce, geid, gavity field, eductin f gavity measuements, efeence suface,
More informationDetermination of a geoid model for Ghana using the Stokes-Helmert method. Michael Adjei Klu. BSc Geodetic Engineering
Deeminaion of a geoid model fo Ghana using he Sokes-Helme mehod by Michael Adjei Klu BSc Geodeic Engineeing A Thesis Submied in Paial Fulfillmen of he Requiemens fo he Degee of Mase of Science in Engineeing
More informationStrees Analysis in Elastic Half Space Due To a Thermoelastic Strain
IOSR Junal f Mathematics (IOSRJM) ISSN: 78-578 Vlume, Issue (July-Aug 0), PP 46-54 Stees Analysis in Elastic Half Space Due T a Themelastic Stain Aya Ahmad Depatment f Mathematics NIT Patna Biha India
More information3-7 FLUIDS IN RIGID-BODY MOTION
3-7 FLUIDS IN IGID-BODY MOTION S-1 3-7 FLUIDS IN IGID-BODY MOTION We ae almost eady to bein studyin fluids in motion (statin in Chapte 4), but fist thee is one cateoy of fluid motion that can be studied
More informationElectric Charge. Electric charge is quantized. Electric charge is conserved
lectstatics lectic Chage lectic chage is uantized Chage cmes in incements f the elementay chage e = ne, whee n is an intege, and e =.6 x 0-9 C lectic chage is cnseved Chage (electns) can be mved fm ne
More informationMEEN 617 Handout #11 MODAL ANALYSIS OF MDOF Systems with VISCOUS DAMPING
MEEN 67 Handou # MODAL ANALYSIS OF MDOF Sysems wih VISCOS DAMPING ^ Symmeic Moion of a n-dof linea sysem is descibed by he second ode diffeenial equaions M+C+K=F whee () and F () ae n ows vecos of displacemens
More informationβ A Constant-G m Biasing
p 2002 EE 532 Anal IC Des II Pae 73 Cnsan-G Bas ecall ha us a PTAT cuen efeence (see p f p. 66 he nes) bas a bpla anss pes cnsan anscnucance e epeaue (an als epenen f supply lae an pcess). Hw h we achee
More informationHotelling s Rule. Therefore arbitrage forces P(t) = P o e rt.
Htelling s Rule In what fllws I will use the tem pice t dente unit pfit. hat is, the nminal mney pice minus the aveage cst f pductin. We begin with cmpetitin. Suppse that a fim wns a small pa, a, f the
More informationMATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH
Fundamenal Jounal of Mahemaical Phsics Vol 3 Issue 013 Pages 55-6 Published online a hp://wwwfdincom/ MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH Univesias
More informationAP Physics 1 MC Practice Kinematics 1D
AP Physics 1 MC Pracice Kinemaics 1D Quesins 1 3 relae w bjecs ha sar a x = 0 a = 0 and mve in ne dimensin independenly f ne anher. Graphs, f he velciy f each bjec versus ime are shwn belw Objec A Objec
More informationSuperluminal Near-field Dipole Electromagnetic Fields. 1 Introduction. 2 Analysis of electric dipole. 2.1 General solution
Supeluinal Nea-field Diple Eleanei Fields Willia D. Wale KTH-Visby Caéaan SE-6 7 Visby, Sweden Eail: bill@visby.h.se Pesened a: Inenainal Wshp Lenz Gup, CPT and Neuins Zaaeas, Mexi, June -6, 999 Induin
More informationLecture 5. Chapter 3. Electromagnetic Theory, Photons, and Light
Lecue 5 Chape 3 lecomagneic Theo, Phoons, and Ligh Gauss s Gauss s Faada s Ampèe- Mawell s + Loen foce: S C ds ds S C F dl dl q Mawell equaions d d qv A q A J ds ds In mae fields ae defined hough ineacion
More information156 There are 9 books stacked on a shelf. The thickness of each book is either 1 inch or 2
156 Thee ae 9 books sacked on a shelf. The hickness of each book is eihe 1 inch o 2 F inches. The heigh of he sack of 9 books is 14 inches. Which sysem of equaions can be used o deemine x, he numbe of
More informationLow-complexity Algorithms for MIMO Multiplexing Systems
Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. :
More informationYield Estimation for a Single Purpose Multi-Reservoir System Using LP Based Yield Model
Junal f Wae Reuce and Pecin, 013, 5, 8-34 hp://dx.di.g/10.436/ap.013.57a005 Publihed Online July 013 (hp://.cip.g/unal/ap) Yield Eimain f a Single Pupe Muli-Reevi Syem Uing LP Baed Yield Mdel Deepak V.
More informationNSEP EXAMINATION
NSE 00-0 EXAMINATION CAEE OINT INDIAN ASSOCIATION OF HYSICS TEACHES NATIONAL STANDAD EXAMINATION IN HYSICS 00-0 Tal ie : 0 inues (A-, A- & B) AT - A (Tal Maks : 80) SUB-AT A- Q. Displaceen f an scillaing
More informationA) N B) 0.0 N C) N D) N E) N
Cdinat: H Bahluli Sunday, Nvembe, 015 Page: 1 Q1. Five identical pint chages each with chage =10 nc ae lcated at the cnes f a egula hexagn, as shwn in Figue 1. Find the magnitude f the net electic fce
More informationThe shortest path between two truths in the real domain passes through the complex domain. J. Hadamard
Complex Analysis R.G. Halbud R.Halbud@ucl.ac.uk Depamen of Mahemaics Univesiy College London 202 The shoes pah beween wo uhs in he eal domain passes hough he complex domain. J. Hadamad Chape The fis fundamenal
More informationLecture 17: Kinetics of Phase Growth in a Two-component System:
Lecue 17: Kineics of Phase Gowh in a Two-componen Sysem: descipion of diffusion flux acoss he α/ ineface Today s opics Majo asks of oday s Lecue: how o deive he diffusion flux of aoms. Once an incipien
More informationAnnouncements Candidates Visiting Next Monday 11 12:20 Class 4pm Research Talk Opportunity to learn a little about what physicists do
Wed., /11 Thus., /1 Fi., /13 Mn., /16 Tues., /17 Wed., /18 Thus., /19 Fi., / 17.7-9 Magnetic Field F Distibutins Lab 5: Bit-Savat B fields f mving chages (n quiz) 17.1-11 Pemanent Magnets 18.1-3 Mic. View
More informationMechanics and Special Relativity (MAPH10030) Assignment 3
(MAPH0030) Assignment 3 Issue Date: 03 Mach 00 Due Date: 4 Mach 00 In question 4 a numeical answe is equied with pecision to thee significant figues Maks will be deducted fo moe o less pecision You may
More informationCHAPTER 24 GAUSS LAW
CHAPTR 4 GAUSS LAW LCTRIC FLUX lectic flux is a measue f the numbe f electic filed lines penetating sme suface in a diectin pependicula t that suface. Φ = A = A csθ with θ is the angle between the and
More informationWORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done
More informationOutline. Steady Heat Transfer with Conduction and Convection. Review Steady, 1-D, Review Heat Generation. Review Heat Generation II
Steady Heat ansfe ebuay, 7 Steady Heat ansfe wit Cnductin and Cnvectin ay Caett Mecanical Engineeing 375 Heat ansfe ebuay, 7 Outline eview last lectue Equivalent cicuit analyses eview basic cncept pplicatin
More informationThe Gradient and Applications This unit is based on Sections 9.5 and 9.6, Chapter 9. All assigned readings and exercises are from the textbook
The Gadient and Applicatins This unit is based n Sectins 9.5 and 9.6 Chapte 9. All assigned eadings and eecises ae fm the tetbk Objectives: Make cetain that u can define and use in cntet the tems cncepts
More informationCHAPTER 5: Circular Motion; Gravitation
CHAPER 5: Cicula Motion; Gavitation Solution Guide to WebAssign Pobles 5.1 [1] (a) Find the centipetal acceleation fo Eq. 5-1.. a R v ( 1.5 s) 1.10 1.4 s (b) he net hoizontal foce is causing the centipetal
More informationThe Components of Vector B. The Components of Vector B. Vector Components. Component Method of Vector Addition. Vector Components
Upcming eens in PY05 Due ASAP: PY05 prees n WebCT. Submiing i ges yu pin ward yur 5-pin Lecure grade. Please ake i seriusly, bu wha cuns is wheher r n yu submi i, n wheher yu ge hings righ r wrng. Due
More informationTotal Deformation and its Role in Heavy Precipitation Events Associated with Deformation-Dominant Flow Patterns
ADVANCES IN ATMOSPHERIC SCIENCES VOL. 25 NO. 1 2008 11 23 Tal Defmain and is Rle in Heavy Pecipiain Evens Assciaed wih Defmain-Dminan Flw Paens GAO Shuing 1 (påë) YANG Shuai 12 (fl R) XUE Ming 3 (Å ) and
More informationEPr over F(X} AA+ A+A. For AeF, a generalized inverse. ON POLYNOMIAL EPr MATRICES
Intenat. J. Hath. & Math. S. VOL. 15 NO. 2 (1992) 261-266 ON POLYNOMIAL EP MATRICES 261 AR. MEENAKSHI and N. ANANOAM Depatment f Mathematics, Annamalai Univeslty, Annamalainaga- 68 2, Tamll Nadu, INDIA.
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES In igid body kinemaics, we use he elaionships govening he displacemen, velociy and acceleaion, bu mus also accoun fo he oaional moion of he body. Descipion of he moion of igid
More informationDo not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Mathematics Main Seies UG Examination 2015 16 FLUID DYNAMICS WITH ADVANCED TOPICS MTH-MD59 Time allowed: 3 Hous Attempt QUESTIONS 1 and 2, and THREE othe questions.
More informationSection 4.2 Radians, Arc Length, and Area of a Sector
Sectin 4.2 Radian, Ac Length, and Aea f a Sect An angle i fmed by tw ay that have a cmmn endpint (vetex). One ay i the initial ide and the the i the teminal ide. We typically will daw angle in the cdinate
More information10.7 Temperature-dependent Viscoelastic Materials
Secin.7.7 Temperaure-dependen Viscelasic Maerials Many maerials, fr example plymeric maerials, have a respnse which is srngly emperaure-dependen. Temperaure effecs can be incrpraed in he hery discussed
More informationOn orthonormal Bernstein polynomial of order eight
Oen Science Junal f Mathematic and Alicatin 2014; 22): 15-19 Publihed nline Ail 20, 2014 htt://www.enciencenline.cm/junal/jma) On thnmal Bentein lynmial f de eight Suha N. Shihab, Tamaa N. Naif Alied Science
More informationChapter 7. Interference
Chape 7 Inefeence Pa I Geneal Consideaions Pinciple of Supeposiion Pinciple of Supeposiion When wo o moe opical waves mee in he same locaion, hey follow supeposiion pinciple Mos opical sensos deec opical
More informationDetermining 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 investigation
More informationKinematics Review Outline
Kinemaics Review Ouline 1.1.0 Vecrs and Scalars 1.1 One Dimensinal Kinemaics Vecrs have magniude and direcin lacemen; velciy; accelerain sign indicaes direcin + is nrh; eas; up; he righ - is suh; wes;
More informationExample 11: The man shown in Figure (a) pulls on the cord with a force of 70
Chapte Tw ce System 35.4 α α 100 Rx cs 0.354 R 69.3 35.4 β β 100 Ry cs 0.354 R 111 Example 11: The man shwn in igue (a) pulls n the cd with a fce f 70 lb. Repesent this fce actin n the suppt A as Catesian
More information1) Consider an object of a parabolic shape with rotational symmetry z
Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Mechanics (Stömningsläa), 01-06-01, kl 9.00-15.00 jälpmedel: Students may use any book including the tetbook Lectues on Fluid Dynamics.
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationOn Control Problem Described by Infinite System of First-Order Differential Equations
Ausalian Jounal of Basic and Applied Sciences 5(): 736-74 ISS 99-878 On Conol Poblem Descibed by Infinie Sysem of Fis-Ode Diffeenial Equaions Gafujan Ibagimov and Abbas Badaaya J'afau Insiue fo Mahemaical
More informationCombinatorial Approach to M/M/1 Queues. Using Hypergeometric Functions
Inenaional Mahemaical Foum, Vol 8, 03, no 0, 463-47 HIKARI Ld, wwwm-hikaicom Combinaoial Appoach o M/M/ Queues Using Hypegeomeic Funcions Jagdish Saan and Kamal Nain Depamen of Saisics, Univesiy of Delhi,
More informationFall 2016 Semester METR 3113 Atmospheric Dynamics I: Introduction to Atmospheric Kinematics and Dynamics
Fall 06 Semeste METR 33 Atmospheic Dynamics I: Intoduction to Atmospheic Kinematics Dynamics Lectue 7 Octobe 3 06 Topics: Scale analysis of the equations of hoizontal motion Geostophic appoximation eostophic
More informationScratch Ticket Game Closing Analysis SUMMARY REPORT
TEXAS LTTERY ISSI Scach Tice Game lsig Aalysis SUARY REPRT Scach Tice Ifmai mpleed 1/ 3/ 216 Game# 16891 fimed Pacs 4, 613 Game ame Lucy Bucsl Acive Pacs 3, 29 Quaiy Pied 11, 21, 1 aehuse Pacs 1, 222 Pice
More informationAST1100 Lecture Notes
AST00 Lecue Noes 5 6: Geneal Relaiviy Basic pinciples Schwazschild geomey The geneal heoy of elaiviy may be summaized in one equaion, he Einsein equaion G µν 8πT µν, whee G µν is he Einsein enso and T
More informationMicroelectronics Circuit Analysis and Design. ac Equivalent Circuit for Common Emitter. Common Emitter with Time-Varying Input
Micelectnics Cicuit Analysis and Design Dnald A. Neamen Chapte 6 Basic BJT Amplifies In this chapte, we will: Undestand the pinciple f a linea amplifie. Discuss and cmpae the thee basic tansist amplifie
More informationControl Volume Derivation
School of eospace Engineeing Conol Volume -1 Copyigh 1 by Jey M. Seizman. ll ighs esee. Conol Volume Deiaion How o cone ou elaionships fo a close sysem (conol mass) o an open sysem (conol olume) Fo mass
More informationSections 3.1 and 3.4 Exponential Functions (Growth and Decay)
Secions 3.1 and 3.4 Eponenial Funcions (Gowh and Decay) Chape 3. Secions 1 and 4 Page 1 of 5 Wha Would You Rahe Have... $1million, o double you money evey day fo 31 days saing wih 1cen? Day Cens Day Cens
More informationSTUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE WEIBULL DISTRIBUTION
Inenaional Jounal of Science, Technology & Managemen Volume No 04, Special Issue No. 0, Mach 205 ISSN (online): 2394-537 STUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE
More informationChapter 3 Optical Systems with Annular Pupils
Chapte 3 Optical Systems with Annula Pupils 3 INTRODUCTION In this chapte, we discuss the imaging popeties of a system with an annula pupil in a manne simila to those fo a system with a cicula pupil The
More informationA) (0.46 î ) N B) (0.17 î ) N
Phys10 Secnd Maj-14 Ze Vesin Cdinat: xyz Thusday, Apil 3, 015 Page: 1 Q1. Thee chages, 1 = =.0 μc and Q = 4.0 μc, ae fixed in thei places as shwn in Figue 1. Find the net electstatic fce n Q due t 1 and.
More informationn Power transmission, X rays, lightning protection n Solid-state Electronics: resistors, capacitors, FET n Computer peripherals: touch pads, LCD, CRT
.. Cu-Pl, INE 45- Electmagnetics I Electstatic fields anda Cu-Pl, Ph.. INE 45 ch 4 ECE UPM Maagüe, P me applicatins n Pwe tansmissin, X as, lightning ptectin n lid-state Electnics: esists, capacits, FET
More informationExponential and Logarithmic Equations and Properties of Logarithms. Properties. Properties. log. Exponential. Logarithmic.
Eponenial and Logaihmic Equaions and Popeies of Logaihms Popeies Eponenial a a s = a +s a /a s = a -s (a ) s = a s a b = (ab) Logaihmic log s = log + logs log/s = log - logs log s = s log log a b = loga
More informationApplication of Net Radiation Transfer Method for Optimization and Calculation of Reduction Heat Transfer, Using Spherical Radiation Shields
Wld Applied Sciences Junal (4: 457-46, 00 ISSN 88-495 IDOSI Publicatins, 00 Applicatin f Net Radiatin Tansfe Methd f Optimizatin and Calculatin f Reductin Heat Tansfe, Using Spheical Radiatin Shields Seyflah
More informationLecture-V Stochastic Processes and the Basic Term-Structure Equation 1 Stochastic Processes Any variable whose value changes over time in an uncertain
Lecue-V Sochasic Pocesses and he Basic Tem-Sucue Equaion 1 Sochasic Pocesses Any vaiable whose value changes ove ime in an unceain way is called a Sochasic Pocess. Sochasic Pocesses can be classied as
More informationPHYS PRACTICE EXAM 2
PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,
More informationELECTRIC & MAGNETIC FIELDS I (STATIC FIELDS) ELC 205A
LCTRIC & MAGNTIC FILDS I (STATIC FILDS) LC 05A D. Hanna A. Kils Assciate Pfess lectnics & Cmmnicatins ngineeing Depatment Faclty f ngineeing Cai Univesity Fall 0 f Static lecticity lectic & Magnetic Fields
More informationWavefront healing operators for improving reflection coherence
Wavefon healing opeaos fo impoving eflecion coheence David C. Henley Wavefon healing ABSTRACT Seismic eflecion image coninuiy is ofen advesely affeced by inadequae acquisiion o pocessing pocedues by he
More informationChapter 31 Faraday s Law
Chapte 31 Faaday s Law Change oving --> cuent --> agnetic field (static cuent --> static agnetic field) The souce of agnetic fields is cuent. The souce of electic fields is chage (electic onopole). Altenating
More information1. Show that if the angular momentum of a boby is determined with respect to an arbitrary point A, then. r r r. H r A can be expressed by H r r r r
1. Shw that if the angula entu f a bb is deteined with espect t an abita pint, then H can be epessed b H = ρ / v + H. This equies substituting ρ = ρ + ρ / int H = ρ d v + ρ ( ω ρ ) d and epanding, nte
More informationFig. 1S. The antenna construction: (a) main geometrical parameters, (b) the wire support pillar and (c) the console link between wire and coaxial
a b c Fig. S. The anenna consucion: (a) ain geoeical paaees, (b) he wie suppo pilla and (c) he console link beween wie and coaial pobe. Fig. S. The anenna coss-secion in he y-z plane. Accoding o [], he
More informationExtremal problems for t-partite and t-colorable hypergraphs
Exemal poblems fo -paie and -coloable hypegaphs Dhuv Mubayi John Talbo June, 007 Absac Fix ineges and an -unifom hypegaph F. We pove ha he maximum numbe of edges in a -paie -unifom hypegaph on n veices
More informationINVERSE QUANTUM STATES OF HYDROGEN
INVERSE QUANTUM STATES OF HYDROGEN Rnald C. Bugin Edgecmbe Cmmunity Cllege Rcky Munt, Nth Calina 780 bugin@edgecmbe.edu ABSTRACT The pssible existence f factinal quantum states in the hydgen atm has been
More informationIntroduction. Electrostatics
UNIVESITY OF TECHNOLOGY, SYDNEY FACULTY OF ENGINEEING 4853 Electmechanical Systems Electstatics Tpics t cve:. Culmb's Law 5. Mateial Ppeties. Electic Field Stength 6. Gauss' Theem 3. Electic Ptential 7.
More informationAY 7A - Fall 2010 Section Worksheet 2 - Solutions Energy and Kepler s Law
AY 7A - Fall 00 Section Woksheet - Solutions Enegy and Keple s Law. Escape Velocity (a) A planet is obiting aound a sta. What is the total obital enegy of the planet? (i.e. Total Enegy = Potential Enegy
More informationNeutron Slowing Down Distances and Times in Hydrogenous Materials. Erin Boyd May 10, 2005
Neu Slwig Dw Disaces ad Times i Hydgeus Maeials i Byd May 0 005 Oulie Backgud / Lecue Maeial Neu Slwig Dw quai Flux behavi i hydgeus medium Femi eame f calculaig slwig dw disaces ad imes. Bief deivai f
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.265/15.070J Fall 2013 Lecture 15 10/30/2013. Ito integral for simple processes
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.65/15.7J Fall 13 Lecure 15 1/3/13 I inegral fr simple prcesses Cnen. 1. Simple prcesses. I ismery. Firs 3 seps in cnsrucing I inegral fr general prcesses 1 I inegral
More information