EE 570: Location and Navigation: Theory & Practice
|
|
- Gabriel Fields
- 6 years ago
- Views:
Transcription
1 EE 570: ocato ad Navgato: Thory & Practc Navgato Mathmatcs Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 1 of 15
2 Navgato Mathmatcs : Coordat Fram Trasformatos Dtrm th dtald kmatc rlatoshps tw th 4 major frams of trst Th Earth-Ctrd Irtal (ECI) Coordat Fram (fram) Th Earth-Ctrd Earth-Fxd (ECEF) Coordat Fram (-fram) Th ocal Navgato (Nav) Coordat Fram (-fram) Th Body Coordat Fram (-fram) Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 2 of 15
3 Navgato Mathmatcs : Coordat Fram Trasformatos - ECI/ECEF Rlatoshp Btw th ECI ad ECEF Frams ECI & ECEF hav co-locatd orgs o r = r = r = 0 Th x, y, ad z axs of th ECI & ECEF frams ar cocdt at tm t 0 Th ECEF fram rotats aout th commo z-axs at a fxd rat (ω ) o Igorg mor spd varatos (prcsso & utato) ω = µrad/s (WGS84) whch s 15/hr Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 3 of 15
4 Navgato Mathmatcs : Coordat Fram Trasformatos - ECI/ECEF Th agular vlocty ad acclrato ar: 0 0 Th agl of rotato s tt 0 t GMST GMST: Grwch Ma Sdral tm Th ortato of fram {} wrt fram {} coms Cos( ) S( ) C R 0, S( ) Cos( ) 0 z NOTE: ω = ω Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 4 of 15
5 Navgato Mathmatcs : Coordat Fram Trasformatos - ECEF/Nav Dscrptos wrt th Navgato fram Ortato of th -fram wrt th -fram C R R z y,, 90 cos s 0 s 0 cos s cos cos 0 s Godtc at = ad Godtc o = s s c s c c cos s cos cos s s s s c c cos s cos s cos c 0 0 s s Compact Notato: cos θ = c θ & s θ = s θ Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 5 of 15
6 Navgato Mathmatcs : Coordat Fram Trasformatos - ECEF/Nav Agular vlocty of th -fram wrt th -fram rsolvd th -fram as a Skw-Symmtrc matrx T C C s s c c c c s c s c s s c c c s c s s s s c c s s c c s s 0 0 c c s 0 cos 0 s cos s 0 Th agular vlocty vctor s cos cos T C s C C C T Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 6 of 15
7 Navgato Mathmatcs : Coordat Fram Trasformatos - ECI/ECEF/Nav Hc th ortato of th -fram wrt th -fram coms c s 0 s c s c c C CC s c 0 s s c c s c 0 s cos 0 s s cos s cos cos s s cos cos s Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 7 of 15
8 Navgato Mathmatcs : Coordat Fram Trasformatos - ECI/ECEF/Nav Th agular vlocty of th -fram wrt th -fram rsolvd th -fram s: C??? 0 Cos( ) S( ) 0 s 0 S( ) Cos( ) 0 cos s cos Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 8 of 15
9 Navgato Mathmatcs : Coordat Fram Trasformatos - ECEF/Nav Th vctor from org of th -fram to th -fram org rsolvd th -fram (from th last lctur) RE h Cos( ) Cos( ) r RE h Cos( ) S( ) 2 RE (1 ) h S( ) r Orgs of th {} ad {} frams ar th sam Th vlocty of th -fram wrt th -fram rsolvd th -fram (s hadout#1 for proof) v d r dt r r r h h Cos( ) S( ) S( ) Cos( ) Cos( ) RN h S( ) S( ) Cos( ) Cos( ) S( ) Cos( ) RE h Cos( ) 0 S( ) h Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 9 of 15
10 Navgato Mathmatcs : Coordat Fram Trasformatos - ECEF/Nav Rcallg th form of C suggsts that v ad hc, RN h Cos( ) C R h h E C v? v RN h Cos( )R h E h Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 10 of 15
11 Navgato Mathmatcs : Coordat Fram Trasformatos - ECEF/Nav Rstatg v as ad rcallg that Suggsts that v N, N Cos( ) RE h v, E h v D, R h v v ta cos s, E RE h v, R h v R h N N, E E Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 11 of 15
12 Navgato Mathmatcs : Coordat Fram Trasformatos Body Fram Dscrptos wrt th Body fram Ortato of th -fram wrt th -fram trms of rlatv yaw(), ptch(), th roll() agls C R R R z y x,,, c s 0 c 0 s s c c s s 0 c 0 s c y c c c s s c s c c s s s c s c c s s s c s s c s s c s c c x z Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 12 of 15
13 Navgato Mathmatcs : Coordat Fram Trasformatos Body Fram Th agular vlocty of th -fram wrt th -fram rsolvd/coordatzd th -fram C C C Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 13 of 15
14 Navgato Mathmatcs : Coordat Fram Trasformatos Body Fram Posto vctors to th org of th ody fram Th orgs of th ody ad Nav frams ar co-cdt r 0 Th orgs of th ECI ad ECEF frams ar co-cdt r r r r Vlocty of th -fram wrt th -fram rsolvd th - fram o Cas #2: A movg pot a rotatg fram v d r dt C r C v C r v d Cr dt Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 14 of 15
15 Navgato Mathmatcs : Coordat Fram Trasformatos Body Fram Acclrato of th -fram wrt th -fram rsolvd th -fram o Cas #2: A movg pot a rotatg fram a d v dt C r v C C r 2 v a d C r v dt r r v Thursay 7 F 2013 NMT EE 570: ocato ad Navgato: Thory & Practc Sld 15 of 15
EE 570: Location and Navigation: Theory & Practice
EE 570: Locaton and Navgaton: Thor & Practc Navgaton Snsors and INS Mchanaton Thursda 8 F 013 NMT EE 570: Locaton and Navgaton: Thor & Practc Sld 1 of 10 Navgaton Snsors and INS Mchanaton Navgaton Equatons
More informationNavigation Mathematics: Kinematics (Coordinate Frame Transformation) EE 570: Location and Navigation
Lecture Navigation Mathematics: Kinematics (Coordinate Frame Transformation) EE 570: Location and Navigation Lecture Notes Update on Feruary 16, 2016 Aly El-Osery and Kevin Wedeward, Electrical Engineering
More informationEE 570: Location and Navigation: Theory & Practice
EE 570: Locatio ad Naigatio: Thory & Practic Naigatio Ssors ad INS Mchaizatio NMT EE 570: Locatio ad Naigatio: Thory & Practic Slid 1 of 13 Naigatio Ssors ad INS Mchaizatio Naigatio Equatios Cas 3: Na
More informationEE 570: Location and Navigation
EE 570: Location and Navigation Navigation Mathematics: Coordinate Frames Kevin Wedeward Aly El-Osery Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen
More informationNMT EE570 Location and Navigation
NMT EE57 Location and Navigation Som Dfinitions Handout# Th ECI to ECEF Fram Orintation and Angular Vlocity: Th angular vlocity of th ECEF fram with rspct to th ECI fram (Ωi 7.9567 Μrad/sc): In[4]: Ωi,
More informationEE 570: Location and Navigation: Theory & Practice
EE 570: Locaton and Navgaton: Theory & Practce Navgaton Sensors and INS Mechanzaton Tuesday 26 Fe 2013 NMT EE 570: Locaton and Navgaton: Theory & Practce Slde 1 of 14 Navgaton Sensors and INS Mechanzaton
More informationEE 570: Location and Navigation: Theory & Practice
EE 57: Location and Navigation: Thory & Practic Navigation Mathmatics Tusday 5 Fb 213 NMT EE 57: Location and Navigation: Thory & Practic Slid 1 of 12 Navigation Mathmatics : Earth surfac and Gravity -
More information3.4 Properties of the Stress Tensor
cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato
More informationCourse 10 Shading. 1. Basic Concepts: Radiance: the light energy. Light Source:
Cour 0 Shadg Cour 0 Shadg. Bac Coct: Lght Sourc: adac: th lght rg radatd from a ut ara of lght ourc or urfac a ut old agl. Sold agl: $ # r f lght ourc a ot ourc th ut ara omttd abov dfto. llumato: lght
More informationDepartment of Mathematics and Statistics Indian Institute of Technology Kanpur MSO202A/MSO202 Assignment 3 Solutions Introduction To Complex Analysis
Dpartmt of Mathmatcs ad Statstcs Ida Isttut of Tchology Kapur MSOA/MSO Assgmt 3 Solutos Itroducto To omplx Aalyss Th problms markd (T) d a xplct dscusso th tutoral class. Othr problms ar for hacd practc..
More informationLECTURE 6 TRANSFORMATION OF RANDOM VARIABLES
LECTURE 6 TRANSFORMATION OF RANDOM VARIABLES TRANSFORMATION OF FUNCTION OF A RANDOM VARIABLE UNIVARIATE TRANSFORMATIONS TRANSFORMATION OF RANDOM VARIABLES If s a rv wth cdf F th Y=g s also a rv. If w wrt
More informationUnbalanced Panel Data Models
Ubalacd Pal Data odls Chaptr 9 from Baltag: Ecoomtrc Aalyss of Pal Data 5 by Adrás alascs 4448 troducto balacd or complt pals: a pal data st whr data/obsrvatos ar avalabl for all crosssctoal uts th tr
More informationComplex Numbers. Prepared by: Prof. Sunil Department of Mathematics NIT Hamirpur (HP)
th Topc Compl Nmbrs Hyprbolc fctos ad Ivrs hyprbolc fctos, Rlato btw hyprbolc ad crclar fctos, Formla of hyprbolc fctos, Ivrs hyprbolc fctos Prpard by: Prof Sl Dpartmt of Mathmatcs NIT Hamrpr (HP) Hyprbolc
More informationEE 570: Location and Navigation
EE 570: Location and Navigation Navigation Equations: Nav Mechanization Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen
More informationSecond Handout: The Measurement of Income Inequality: Basic Concepts
Scod Hadout: Th Masurmt of Icom Iqualty: Basc Cocpts O th ormatv approach to qualty masurmt ad th cocpt of "qually dstrbutd quvalt lvl of com" Suppos that that thr ar oly two dvduals socty, Rachl ad Mart
More informationLecture 1: Empirical economic relations
Ecoomcs 53 Lctur : Emprcal coomc rlatos What s coomtrcs? Ecoomtrcs s masurmt of coomc rlatos. W d to kow What s a coomc rlato? How do w masur such a rlato? Dfto: A coomc rlato s a rlato btw coomc varabls.
More informationPion Production via Proton Synchrotron Radiation in Strong Magnetic Fields in Relativistic Quantum Approach
Po Producto va Proto Sychrotro Radato Strog Magtc Flds Rlatvstc Quatum Approach Partcl Productos TV Ergy Rgo Collaborators Toshtaka Kajo Myog-K Chou Grad. J. MATHEWS Tomoyuk Maruyama BRS. Nho Uvrsty NaO,
More informationManipulator Dynamics. Amirkabir University of Technology Computer Engineering & Information Technology Department
Mapulator Dyamcs mrkabr Uversty of echology omputer Egeerg formato echology Departmet troducto obot arm dyamcs deals wth the mathematcal formulatos of the equatos of robot arm moto. hey are useful as:
More informationIn 1991 Fermat s Last Theorem Has Been Proved
I 99 Frmat s Last Thorm Has B Provd Chu-Xua Jag P.O.Box 94Bg 00854Cha Jcxua00@s.com;cxxxx@6.com bstract I 67 Frmat wrot: It s mpossbl to sparat a cub to two cubs or a bquadrat to two bquadrats or gral
More informationCarbonyl Groups. University of Chemical Technology, Beijing , PR China;
Electroc Supplemetary Materal (ESI) for Physcal Chemstry Chemcal Physcs Ths joural s The Ower Socetes 0 Supportg Iformato A Theoretcal Study of Structure-Solublty Correlatos of Carbo Doxde Polymers Cotag
More informationA Note on Estimability in Linear Models
Intrnatonal Journal of Statstcs and Applcatons 2014, 4(4): 212-216 DOI: 10.5923/j.statstcs.20140404.06 A Not on Estmablty n Lnar Modls S. O. Adymo 1,*, F. N. Nwob 2 1 Dpartmnt of Mathmatcs and Statstcs,
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationEE 570: Location and Navigation
EE 570: Location and Navigation Error Mechanization (ECEF) Aly El-Osery Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA April 11, 2013 Attitude Velocity Gravity Position Summary
More informationTotal Prime Graph. Abstract: We introduce a new type of labeling known as Total Prime Labeling. Graphs which admit a Total Prime labeling are
Itratoal Joural Of Computatoal Egrg Rsarch (crol.com) Vol. Issu. 5 Total Prm Graph M.Rav (a) Ramasubramaa 1, R.Kala 1 Dpt.of Mathmatcs, Sr Shakth Isttut of Egrg & Tchology, Combator 641 06. Dpt. of Mathmatcs,
More information' 1.00, has the form of a rhomb with
Problm I Rflcto ad rfracto of lght A A trstg prsm Th ma scto of a glass prsm stuatd ar ' has th form of a rhomb wth A th yllow bam of moochromatc lght propagatg towards th prsm paralll wth th dagoal AC
More informationCorrelation in tree The (ferromagnetic) Ising model
5/3/00 :\ jh\slf\nots.oc\7 Chaptr 7 Blf propagato corrlato tr Corrlato tr Th (frromagtc) Isg mol Th Isg mol s a graphcal mol or par ws raom Markov fl cosstg of a urct graph wth varabls assocat wth th vrtcs.
More informationEE 565: Position, Navigation and Timing
EE 565: Position, Navigation and Timing Navigation Mathematics: Angular and Linear Velocity Kevin Wedeward Aly El-Osery Electrical Engineering Department New Mexico Tech Socorro, New Mexico, USA In Collaboration
More informationPhysics 256: Lecture 2. Physics
Physcs 56: Lctur Intro to Quantum Physcs Agnda for Today Complx Numbrs Intrfrnc of lght Intrfrnc Two slt ntrfrnc Dffracton Sngl slt dffracton Physcs 01: Lctur 1, Pg 1 Constructv Intrfrnc Ths wll occur
More informationRECURSIVE FORMULATION FOR MULTIBODY DYNAMICS
ultbody Dyamcs Lecture Uversty of okyo, Japa Dec. 8, 25 RECURSIVE FORULAION FOR ULIODY DYNAICS Lecturer: Sug-Soo m Professor, Dept. of echatrocs Egeerg, orea Vstg Professor, Ceter for Collaboratve Research
More informationAttitude Determination GPS/INS Integration System Design Using Triple Difference Technique
Joural of Elctrcal Egrg & Tchology Vol. 7, No., pp. 1~, 1 1 http://dx.do.org/1.37/jeet.1.7..1 Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu Sag Ho Oh*, Dog-Hwa Hwag, Chask Park** ad Sag
More informationPlanar Rigid Body Kinematics Homework
Chapter 2: Planar Rigid ody Kinematics Homework Chapter 2 Planar Rigid ody Kinematics Homework Freeform c 2018 2-1 Chapter 2: Planar Rigid ody Kinematics Homework 2-2 Freeform c 2018 Chapter 2: Planar
More informationDSP-First, 2/e. LECTURE # CH2-3 Complex Exponentials & Complex Numbers TLH MODIFIED. Aug , JH McClellan & RW Schafer
DSP-First, / TLH MODIFIED LECTURE # CH-3 Complx Exponntials & Complx Numbrs Aug 016 1 READING ASSIGNMENTS This Lctur: Chaptr, Scts. -3 to -5 Appndix A: Complx Numbrs Complx Exponntials Aug 016 LECTURE
More informationStatics. Consider the free body diagram of link i, which is connected to link i-1 and link i+1 by joint i and joint i-1, respectively. = r r r.
Statcs Th cotact btw a mapulato ad ts vomt sults tactv ocs ad momts at th mapulato/vomt tac. Statcs ams at aalyzg th latoshp btw th actuato dv tous ad th sultat oc ad momt appld at th mapulato dpot wh
More informationFlight Dynamics & Control Equations of Motion of 6 dof Rigid Aircraft-Kinematics
Flight Dynamic & Control Equation of Motion of 6 dof Rigid Aircraft-Kinematic Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline Rotation Matrix Angular Velocity Euler
More informationCOMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES
COMPLEX NUMBERS AND ELEMENTARY FUNCTIONS OF COMPLEX VARIABLES DEFINITION OF A COMPLEX NUMBER: A umbr of th form, whr = (, ad & ar ral umbrs s calld a compl umbr Th ral umbr, s calld ral part of whl s calld
More informationOn the Possible Coding Principles of DNA & I Ching
Sctfc GOD Joural May 015 Volum 6 Issu 4 pp. 161-166 Hu, H. & Wu, M., O th Possbl Codg Prcpls of DNA & I Chg 161 O th Possbl Codg Prcpls of DNA & I Chg Hupg Hu * & Maox Wu Rvw Artcl ABSTRACT I ths rvw artcl,
More information( ) Two-Dimensional Experimental Kinematics. Notes_05_02 1 of 9. Digitize locations of landmarks { r } Pk
Notes_05_0 o 9 Two-Dmesoal Expermetal Kematcs Dgtze locatos o ladmarks { r } o body or pots to at gve tme t ll pots must be attached to body Use ladmark weghtg actor = pot k s avalable at tme t. Use =
More informationComputational Geometry
Problem efto omputatoal eometry hapter 6 Pot Locato Preprocess a plaar map S. ve a query pot p, report the face of S cotag p. oal: O()-sze data structure that eables O(log ) query tme. pplcato: Whch state
More informationNMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING. Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582
NMT EE 589 & UNM ME 482/582 ROBOT ENGINEERING Dr. Stephen Bruder NMT EE 589 & UNM ME 482/582 4. Moton Knematcs 4.2 Angular Velocty Knematcs Summary From the last lecture we concluded that: If the jonts
More informationLecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e
8/7/018 Cours Instructor Dr. Raymond C. Rumpf Offic: A 337 Phon: (915) 747 6958 E Mail: rcrumpf@utp.du EE 4347 Applid Elctromagntics Topic 3 Skin Dpth & Powr Flow Skin Dpth Ths & Powr nots Flow may contain
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationAotomorphic Functions And Fermat s Last Theorem(4)
otomorphc Fuctos d Frmat s Last Thorm(4) Chu-Xua Jag P. O. Box 94 Bg 00854 P. R. Cha agchuxua@sohu.com bsract 67 Frmat wrot: It s mpossbl to sparat a cub to two cubs or a bquadrat to two bquadrats or gral
More informationSuperbosonization meets Free Probability
Suprbosoato mts Fr Probablty M Zrbaur jot wor wth S Madt Eulr Symposum St Ptrsburg Ju 3 009 Itroducto From momts to cumulats Larg- charactrstc fucto by fr probablty Suprbosoato Applcato to dsordrd scattrg
More information10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D
Comp 35 Introducton to Machn Larnng and Data Mnng Fall 204 rofssor: Ron Khardon Mxtur Modls Motvatd by soft k-mans w dvlopd a gnratv modl for clustrng. Assum thr ar k clustrs Clustrs ar not rqurd to hav
More informationThe Hyperelastic material is examined in this section.
4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):
More informationEE 570: Location and Navigation
EE 570: Location and Navigation Navigation Mathematics: Kinematics (Earth Surface & Gravity Models) Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA
More informationEE 570: Location and Navigation
EE 570: Locatio ad Navigatio Error Mechaizatio (NAV) Aly El-Osery Kevi Wedeward Electrical Egieerig Departmet, New Mexico Tech Socorro, New Mexico, USA I Collaboratio with Stephe Bruder Electrical ad Computer
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationME 501A Seminar in Engineering Analysis Page 1
St Ssts o Ordar Drtal Equatos Novbr 7 St Ssts o Ordar Drtal Equatos Larr Cartto Mcacal Er 5A Sar Er Aalss Novbr 7 Outl Mr Rsults Rvw last class Stablt o urcal solutos Stp sz varato or rror cotrol Multstp
More informationDynamics 12e. Copyright 2010 Pearson Education South Asia Pte Ltd. Chapter 20 3D Kinematics of a Rigid Body
Engineering Mechanics: Dynamics 12e Chapter 20 3D Kinematics of a Rigid Body Chapter Objectives Kinematics of a body subjected to rotation about a fixed axis and general plane motion. Relative-motion analysis
More informationMODEL QUESTION. Statistics (Theory) (New Syllabus) dx OR, If M is the mode of a discrete probability distribution with mass function f
MODEL QUESTION Statstcs (Thory) (Nw Syllabus) GROUP A d θ. ) Wrt dow th rsult of ( ) ) d OR, If M s th mod of a dscrt robablty dstrbuto wth mass fucto f th f().. at M. d d ( θ ) θ θ OR, f() mamum valu
More informationECE 650 1/8. Homework Set 4 - Solutions
ECE 65 /8 Homwork St - Solutions. (Stark & Woods #.) X: zro-man, C X Find G such that Y = GX will b lt. whit. (Will us: G = -/ E T ) Finding -valus for CX: dt = (-) (-) = Finding corrsponding -vctors for
More informationIntroduction to Medical Imaging. Lecture 4: Fourier Theory = = ( ) 2sin(2 ) Introduction
Introduction Introduction to Mdical aging Lctur 4: Fourir Thory Thory dvlopd by Josph Fourir (768-83) Th Fourir transform of a signal s() yilds its frquncy spctrum S(k) Klaus Mullr s() forward transform
More informationT and V be the total kinetic energy and potential energy stored in the dynamic system. The Lagrangian L, can be defined by
From MEC '05 Itrgratg Prosthtcs ad Mdc, Procdgs of th 005 MyoElctrc Cotrols/Powrd Prosthtcs Symposum, hld Frdrcto, Nw Bruswc, Caada, ugust 7-9, 005. EECROMECHNIC NYSIS OF COMPEE RM PROSHESIS (EMS) Prmary
More informationIntroduction to Multicopter Design and Control
Introduction to Multicoptr Dsign and Control Lsson 05 Coordinat Systm and Attitud Rprsntation Quan Quan, Associat Profssor _uaa@uaa.du.cn BUAA Rlial Flight Control Group, http://rfly.uaa.du.cn/ Bihang
More informationα1 α2 Simplex and Rectangle Elements Multi-index Notation of polynomials of degree Definition: The set P k will be the set of all functions:
Smplex ad Rectagle Elemets Mult-dex Notato = (,..., ), o-egatve tegers = = β = ( β,..., β ) the + β = ( + β,..., + β ) + x = x x x x = x x β β + D = D = D D x x x β β Defto: The set P of polyomals of degree
More informationThree-Dimensional Theory of Nonlinear-Elastic. Bodies Stability under Finite Deformations
Appld Mathmatcal Sccs ol. 9 5 o. 43 75-73 HKAR Ltd www.m-hkar.com http://dx.do.org/.988/ams.5.567 Thr-Dmsoal Thory of Nolar-Elastc Bods Stablty udr Ft Dformatos Yu.. Dmtrko Computatoal Mathmatcs ad Mathmatcal
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationLast time. Resistors. Circuits. Question. Quick Quiz. Quick Quiz. ( V c. Which bulb is brighter? A. A B. B. C. Both the same
Last tim Bgin circuits Rsistors Circuits Today Rsistor circuits Start rsistor-capacitor circuits Physical layout Schmatic layout Tu. Oct. 13, 2009 Physics 208 Lctur 12 1 Tu. Oct. 13, 2009 Physics 208 Lctur
More informationSoft k-means Clustering. Comp 135 Machine Learning Computer Science Tufts University. Mixture Models. Mixture of Normals in 1D
Comp 35 Machn Larnng Computr Scnc Tufts Unvrsty Fall 207 Ron Khardon Th EM Algorthm Mxtur Modls Sm-Suprvsd Larnng Soft k-mans Clustrng ck k clustr cntrs : Assocat xampls wth cntrs p,j ~~ smlarty b/w cntr
More informationOn the Hamiltonian of a Multi-Electron Atom
On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making
More informationNumerical Method: Finite difference scheme
Numrcal Mthod: Ft dffrc schm Taylor s srs f(x 3 f(x f '(x f ''(x f '''(x...(1! 3! f(x 3 f(x f '(x f ''(x f '''(x...(! 3! whr > 0 from (1, f(x f(x f '(x R Droppg R, f(x f(x f '(x Forward dffrcg O ( x from
More informationELECTRON-MUON SCATTERING
ELECTRON-MUON SCATTERING ABSTRACT Th lctron charg is considrd to b distributd or xtndd in spac. Th diffrntial of th lctron charg is st qual to a function of lctron charg coordinats multiplid by a four-dimnsional
More informationReview Exam II Complex Analysis
Revew Exam II Complex Aalyss Uderled Propostos or Theorems: Proofs May Be Asked for o Exam Chapter 3. Ifte Seres Defto: Covergece Defto: Absolute Covergece Proposto. Absolute Covergece mples Covergece
More informationLecture II: Rigid-Body Physics
Rigid-Body Motion Previously: Point dimensionless objects moving through a trajectory. Today: Objects with dimensions, moving as one piece. 2 Rigid-Body Kinematics Objects as sets of points. Relative distances
More information2. Background Material
S. Blair Sptmbr 3, 003 4. Background Matrial Th rst of this cours dals with th gnration, modulation, propagation, and ction of optical radiation. As such, bic background in lctromagntics and optics nds
More informationCOMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP
ISAHP 00, Bal, Indonsa, August -9, 00 COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP Chkako MIYAKE, Kkch OHSAWA, Masahro KITO, and Masaak SHINOHARA Dpartmnt of Mathmatcal Informaton Engnrng
More informationThe Frequency Response of a Quarter-Wave Matching Network
4/1/29 Th Frquncy Rsons o a Quartr 1/9 Th Frquncy Rsons o a Quartr-Wav Matchg Ntwork Q: You hav onc aga rovidd us with conusg and rhas uslss ormation. Th quartr-wav matchg ntwork has an xact SFG o: a Τ
More informationMulti-linear Systems and Invariant Theory. in the Context of Computer Vision and Graphics. Class 5: Self Calibration. CS329 Stanford University
Mlti-linar Systms and Invariant hory in th ontt of omtr Vision and Grahics lass 5: Slf alibration S39 Stanford Univrsity Amnon Shasha lass 5 Matrial W Will ovr oday h basic qations and conting argmnts
More informationClassical Mechanics Qualifying Exam Solutions Problem 1.
Jauary 4, Uiversity of Illiois at Chicago Departmet of Physics Classical Mechaics Qualifyig Exam Solutios Prolem. A cylider of a o-uiform radial desity with mass M, legth l ad radius R rolls without slippig
More informationNAVIGATION USING LOW COST INERTIAL UNIT (IMU-MEMS) AND GPS RECEIVER WITH APPLICATION OF SIGMA-POINT KALMAN FILTER. Walter Einwoegerer
wogrr W. t al. avgato usg low t rtal ut AIGATIO USIG LOW COST ITIAL UIT (IMU-MMS) A GPS CI WITH APPLICATIO OF SIGMA-POIT KALMA FILT Waltr wogrr IP - Av dos Astroautas 758 CP 7 São José dos Campos SP Brazl
More informationFor more important questions visit :
For mor important qustions visit : www4onocom CHAPTER 5 CONTINUITY AND DIFFERENTIATION POINTS TO REMEMBER A function f() is said to b continuous at = c iff lim f f c c i, lim f lim f f c c c f() is continuous
More informationComputing and Communications -- Network Coding
89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc
More information16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 6: Heat Conduction: Thermal Stresses
16.512, okt Proulon Prof. Manul Martnz-Sanhz Ltur 6: Hat Conduton: Thrmal Str Efft of Sold or Lqud Partl n Nozzl Flow An u n hhly alumnzd old rokt motor. 3 2Al + O 2 Al 2 O 2 3 m.. 2072 C, b.. 2980 C In
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationorbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationA Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationSundials and Linear Algebra
Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.
More informationLecture 14. P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1
Lctur 4 - ucto ods art 3 Quattatv alyss Math, math ad mor math Radg rrt 6. Gorga Tch ECE 3040 - r. la oolttl Quattatv - od Soluto ssumtos stady stat codtos o- dgrat dog 3 o- dmsoal aalyss 4 low- lvl jcto
More informationMCE/EEC 647/747: Robot Dynamics and Control. Lecture 2: Rigid Motions and Homogeneous Transformations
MCE/EEC 647/747: Robot Dynamics and Control Lecture 2: Rigid Motions and Homogeneous Transformations Reading: SHV Chapter 2 Mechanical Engineering Hanz Richter, PhD MCE503 p.1/22 Representing Points, Vectors
More informationNote: Torque is prop. to current Stationary voltage is prop. to speed
DC Mach Cotrol Mathmatcal modl. Armatr ad orq f m m a m m r a a a a a dt d ψ ψ ψ ω Not: orq prop. to crrt Statoary voltag prop. to pd Mathmatcal modl. Fld magtato f f f f d f dt a f ψ m m f f m fλ h torq
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More informationHeisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari
snbrg Modl Sad Mohammad Mahd Sadrnhaad Survsor: Prof. bdollah Langar bstract: n ths rsarch w tr to calculat analtcall gnvalus and gnvctors of fnt chan wth ½-sn artcls snbrg modl. W drov gnfuctons for closd
More informationMOLECULAR VIBRATIONS
MOLECULAR VIBRATIONS Here we wsh to vestgate molecular vbratos ad draw a smlarty betwee the theory of molecular vbratos ad Hückel theory. 1. Smple Harmoc Oscllator Recall that the eergy of a oe-dmesoal
More informationChapter 5. Introduction. Introduction. Introduction. Finite Element Modelling. Finite Element Modelling
Chaptr 5 wo-dimnsional problms using Constant Strain riangls (CS) Lctur Nots Dr Mohd Andi Univrsiti Malasia Prlis EN7 Finit Elmnt Analsis Introction wo-dimnsional init lmnt ormulation ollows th stps usd
More informationOn the Study of Nyquist Contour Handling Sampled-Data Control System Real Poles and Zeros
Rvw Artcl O th Study of Nyqust Cotour Hadlg Sapld-Data Cotrol Syst Ral Pols ad Zros Yossaw Wrakahag* Dpartt of Elctrcal ad Coputr Egrg Faculty of Egrg Thaasat Uvrsty Ragst Capus Khlog Nug Khlog Luag Pathu
More informationIntroduction to logistic regression
Itroducto to logstc rgrsso Gv: datast D { 2 2... } whr s a k-dmsoal vctor of ral-valud faturs or attrbuts ad s a bar class labl or targt. hus w ca sa that R k ad {0 }. For ampl f k 4 a datast of 3 data
More informationExchange rates in the long run (Purchasing Power Parity: PPP)
Exchang rats in th long run (Purchasing Powr Parity: PPP) Jan J. Michalk JJ Michalk Th law of on pric: i for a product i; P i = E N/ * P i Or quivalntly: E N/ = P i / P i Ida: Th sam product should hav
More informationFrom Structural Analysis to FEM. Dhiman Basu
From Structural Analyss to FEM Dhman Basu Acknowldgmnt Followng txt books wr consultd whl prparng ths lctur nots: Znkwcz, OC O.C. andtaylor Taylor, R.L. (000). Th FntElmnt Mthod, Vol. : Th Bass, Ffth dton,
More informationWashington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
More informationThe Generalized PV θ View and their applications in the Severe Weather Events
Th Gnralizd PV θ Viw and thir applications in th Svr Wathr Evnts Shouting Gao Institut of Atmosphric Physics, Chins Acadmy of Scincs, Bijing, China OUTLINE Background Gnralizd Potntial Tmpratur Th Scond
More informationAN ANALYTIC EXPRESSION FOR NEAR-FIELD ANGU- LAR GLINT PREDICTION OF RADAR SENSOR USING FAR-FIELD SCATTERING CENTERS MODELS
Progress I Electromagetcs Research M, Vol. 3, 5 38, 13 AN ANALYTIC EXPRESSION FOR NEAR-FIELD ANGU- LAR GLINT PREDICTION OF RADAR SENSOR USING FAR-FIELD SCATTERING CENTERS MODELS Japeg Fa, Shje Fa, Hogq
More informationMulti-Machine Systems with Constant Impedance Loads
Mult-Mach Systms wth Costat Impac Loas Th parts of th txt whch w hav yt to covr clu: Chaptr 3: Systm rspos to small sturbacs Chaptr 6: Lar mols of sychroous machs Chaptrs 7-8: Exctato systms a Effct of
More informationA Method for Determining the Number of Dependent Constraints Using Transformation Parameters of Coordinate Systems Korganbay Sholanov1, a*
Iteratoal Coferece o Mechacs, Materals ad Structural Egeerg (ICMMSE 206) A Method for Determg the Number of Depedet Costrats Usg Trasformato Parameters of Coordate Systems Korgabay Sholaov, a* Karagada
More informationME311 Machine Design
ME311 Machin Dsign Lctur 4: Strss Concntrations; Static Failur W Dornfld 8Sp017 Fairfild Univrsit School of Enginring Strss Concntration W saw that in a curvd bam, th strss was distortd from th uniform
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More information6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved.
6.1 Intgration by Parts and Prsnt Valu Copyright Cngag Larning. All rights rsrvd. Warm-Up: Find f () 1. F() = ln(+1). F() = 3 3. F() =. F() = ln ( 1) 5. F() = 6. F() = - Objctivs, Day #1 Studnts will b
More informationDavisson Germer experiment Announcements:
Davisson Grmr xprimnt Announcmnts: Homwork st 7 is du Wdnsday. Problm solving sssions M3-5, T3-5. Th 2 nd midtrm will b April 7 in MUEN E0046 at 7:30pm. BFFs: Davisson and Grmr. Today w will go ovr th
More informationMoving-Base Gravimetry
Movg-Base Gravmetry Supplemetal Notes to Physcal Geodesy GS6776 Chrstopher Jekel Geodetc Scece he Oho State Uversty Columus, OH 4310 Feruary 016 Arore Scalar Gravmetry Cosder a o-rotatg frame cetered at
More information