Chapters 1 8: Overview
|
|
|
- Beverly Hawkins
- 5 years ago
- Views:
Transcription
1 haptes 8: Oveview hapte : Intoduction haptes 4: Data acquisition haptes 5 8: Data anipulation hapte 5: Vetical iage hapte : Iage coodinate easueents and efineent hapte 7: Matheatical odel and bundle block adjustent hapte 8: heo of oientation & photogaetic tiangulation his chapte will cove oe details about the bundle adjustent pocedue E 59700: Digital Photogaetic Sstes an F. Habib
2 E 59700: hapte 9 Photogaetic Bundle djustent E 59700: Digital Photogaetic Sstes an F. Habib
3 Oveview Photogaetic point positioning Photogaetic bundle adjustent Stuctue of the design and noal atices Sequential estiation of the unknown paaetes Sequential building of the noal equation ati Rules of thub fo the epected pecision fo a bundle adjustent pocedue Special cases: Resection, intesection, and steeo-pai oientation E 59700: Digital Photogaetic Sstes an F. Habib
4 Photogaetic Point Positioning z c Z Pespective ente c Y a a a c X Z Y X f ( X, Y, Z, IOPs, EOPs) a f ( X, Y, Z, IOPs, EOPs) a E 59700: Digital Photogaetic Sstes 4 an F. Habib
5 Photogaetic Point Positioning GSS /IS Y Z a X Y Z X a' aea Diect Indiect Senso Geo-efeencing Oientation E 59700: Digital Photogaetic Sstes 5 an F. Habib
6 ollineait Equations: Stochastic Model ( X X ) ( Y Y ) ( Z Z ) c dist e O O O a p ( X XO) ( Y YO) ( Z ZO) ( X X ) ( Y Y ) ( Z Z ) c dist e O O O a p ( X XO) ( Y YO) ( Z ZO) e e P ~(0, o ) E 59700: Digital Photogaetic Sstes an F. Habib
7 Distotion Model dist = Radial Lens Distotion + Decentic Lens Distotion + tospheic Refaction + ffine Defoation + etc. dist = Radial Lens Distotion + Decentic Lens Distotion + tospheic Refaction + ffine Defoations + etc. E 59700: Digital Photogaetic Sstes 7 an F. Habib
8 Distotion Paaetes Radial Lens Distotion ( k k 4 k...) Radial Lens Distotion ( k k 4 k...) ( p ) { p ( ) p } Decenteing Lens Distotion ( p ) { p p ( )} Decenteing Lens Distotion whee: = {( - p ) + ( - p ) } 0.5 p p E 59700: Digital Photogaetic Sstes 8 an F. Habib
9 ollineait Equations: Involved Paaetes Iage coodinates ( a, a ) Gound coodinates (X, Y,Z ) Eteio Oientation Paaetes (X O, Y O,Z O, ) Inteio Oientation Paaetes: p, p, c aea-elated distotion paaetes that copensate fo deviations fo the assued pespective geoet Radial lens distotion (RLD), Decenteing lens distotion (DLD), ffine defoation (D) E 59700: Digital Photogaetic Sstes 9 an F. Habib
10 Bundle Block djustent E 59700: Digital Photogaetic Sstes 0 an F. Habib
11 Bundle Block djustent 0% Ovelap and 0% side lap E 59700: Digital Photogaetic Sstes an F. Habib
12 Bundle Block djustent Diect elationship between iage and gound coodinates We easue the iage coodinates in the iages of the block. Using the collineait equations, we can elate the iage coodinates, the coesponding gound coodinates, the IOPs, and the EOPs. Using a siultaneous least squaes adjustent, we can solve fo the: he gound coodinates of the tie points, he EOPs, and he IOPs (aea alibation Pocedue). E 59700: Digital Photogaetic Sstes an F. Habib
13 Bundle Block djustent: oncept he iage coodinate easueents and the IOPs define a bundle of light as. he EOPs define the position and the attitude of the bundles in space. Duing the adjustent: he bundles ae otated () and shifted (X o, Y o, Z o ) until: onjugate light as intesect as well as possible at the locations of object space tie points. Light as coesponding to gound contol points pass though the object points as close as possible. E 59700: Digital Photogaetic Sstes an F. Habib
14 Bundle Block djustent: oncept Gound ontol Points ie Points E 59700: Digital Photogaetic Sstes 4 an F. Habib
15 Bundle Block djustent: oncept Gound ontol Points ie Points E 59700: Digital Photogaetic Sstes 5 an F. Habib
16 Least Squaes djustent Gauss Makov Model Obsevation Equations e o P e n n n n n obsevation design vecto noise ati of e vecto ~ unknowns containat ing the obsevation vecto vaiance covaiance (0, o P ) ati of the noise vecto E 59700: Digital Photogaetic Sstes an F. Habib
17 Least Squaes djustent ˆ ( P) P D e~ ˆ ˆ ˆ o ( e ~ o ( P) Pe~ ) / ( n ) E 59700: Digital Photogaetic Sstes 7 an F. Habib
18 on Linea Sste Y a( X ) e a( X ) is the non linea function We use alo Seies Epansion Y a( X Whee : X o Y a( X a X o o e Whee : Y a( X X a ) X a ) X o ) X X o o ( X X ( X X o o ) e (We ignoe highe ode tes) is appoiat e values fo the unknown paaetes ) e o Iteative solution fo the unknown paaetes When should we stop the iteations? E 59700: Digital Photogaetic Sstes 8 an F. Habib
19 Eaple (4 Iages in wo Stips) 4 5 I 4 5 II ontol Point ie Point III IV E 59700: Digital Photogaetic Sstes 9 an F. Habib
20 Balance Between Obsevations & Unknowns ube of obsevations: 4 = 48 obsevations (collineait equations) ube of unknowns: = unknowns Redundanc: ssuptions: IOPs ae assued to be known and eoless. Gound coodinates of the contol points ae eoless. E 59700: Digital Photogaetic Sstes 0 an F. Habib
21 Stuctue of the Design Mati (B) Y = a(x) + e e ~ (0, P - ) Using appoiate values fo the unknown paaetes (X o ) and patial deivatives, the above equations can be lineaized leading to the following equations: 48 = 48 + e 48 e ~ (0, P - ) E 59700: Digital Photogaetic Sstes an F. Habib
22 Stuctue of the Design Mati I II III IV 45 = = E 59700: Digital Photogaetic Sstes an F. Habib
23 Stuctue of the oal Mati I II III IV 4 5 E 59700: Digital Photogaetic Sstes an F. Habib
24 Saple Data caeas. 4 iages. points. ll the points appea in all the iages wo iages wee captued b each caea E 59700: Digital Photogaetic Sstes 4 an F. Habib
25 Stuctue of the oal Mati: Eaple E 59700: Digital Photogaetic Sstes 5 an F. Habib
26 E 59700: Digital Photogaetic Sstes an F. Habib Obsevation Equations ) ~ (0, P e e o n n n n n n n e e n n n n n ube of obsevations (iage coodinate easueents) ube of unknowns: ube of iages (EOPs of the iages) ube of tie points (gound coodinates of tie points) = +
27 E 59700: Digital Photogaetic Sstes an F. Habib 7 oal Equation Mati ) ( ) ( ) ( P P P P
28 E 59700: Digital Photogaetic Sstes an F. Habib 8 oal Equation Mati is a block diagonal ati with sub-blocks along the diagonal. is a block diagonal ati with sub-blocks along the diagonal. ˆ ˆ Question: Unde which cicustances will we deviate fo this stuctue?
29 E 59700: Digital Photogaetic Sstes an F. Habib 9 Reduction of the oal Equation Mati ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ Solving fo fist: < Reebe: is a block diagonal ati with sub-blocks along the diagonal.
30 E 59700: Digital Photogaetic Sstes an F. Habib 0 Reduction of the oal Equation Mati ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ Solving fo fist: < Reebe: is a block diagonal ati with sub-blocks along the diagonal.
31 E 59700: Digital Photogaetic Sstes an F. Habib Reduction of the oal Equation Mati } {ˆ o D } {ˆ D o Vaiance covaiance ati of the estiated paaetes:
32 E 59700: Digital Photogaetic Sstes an F. Habib Building the oal Equation Mati We would like to investigate the possibilit of sequentiall building up the noal equation ati without full building the design ati. (, ) iage coodinates of the i th point in the j th iage i j i j e e
33 E 59700: Digital Photogaetic Sstes an F. Habib oal Equation Mati i j i j i j P P P P P P P P e
34 E 59700: Digital Photogaetic Sstes an F. Habib 4 oal Equation Mati i j i j P P P P P P ote: We cannot solve this ati fo the: he Eteio Oientation Paaetes of the j th iage, and he gound coodinates of the i th point.
35 E 59700: Digital Photogaetic Sstes an F. Habib 5 oal Equation Mati ˆ ˆ Question: How can we sequentiall build the above atices? ssuption: ll the points ae coon to all the iages.
36 E 59700: Digital Photogaetic Sstes an F. Habib -Mati ) ( i i i i i i i i If all the points ae not coon to all the iages: he suation should be caied ove all the points that appea in the iage unde consideation.
37 E 59700: Digital Photogaetic Sstes an F. Habib 7 -Mati ) ( j j j j j j j j If all the points ae not coon to all the iages: he suation should be caied ove all the iages within which the point unde consideation appeas.
38 -Mati ( ) If point i does not appea in iage j : ( ) = 0 E 59700: Digital Photogaetic Sstes 8 an F. Habib
39 E 59700: Digital Photogaetic Sstes an F. Habib 9 - Mati i i i i i i i i j j j j j j j j Once again, we assued that all the points ae coon to all the iages.
40 Pecision of Bundle Block djustent he pecision of the estiated EOPs as well as the gound coodinates of tie points can be obtained b the poduct of: he estiated vaiance coponent, and he invese of the noal equation ati (cofacto ati). he pecision depends on the following factos: Geoetic configuation of the iage block Base-Height atio Iage scale Iage coodinate easueent pecision E 59700: Digital Photogaetic Sstes 40 an F. Habib
41 Pecision of Bundle Block djustent Pecision of a single odel: If we have Bundle block adjustent with additional paaetes that copensate fo vaious distotions Regula blocks with 0%ovelap and 0% side lap Signalized tagets XY Z Z 0.00% of the caea pincipal distance ( and W caeas) 0.004% of the caea pincipal distance (SW caeas) hese pecision values ae given in the iage space E 59700: Digital Photogaetic Sstes 4 an F. Habib
42 aea lassification < 75 oal angle caea () 00 > > 75 Wide angle caea (W) > 00 Supe wide angle caea (SW) E 59700: Digital Photogaetic Sstes 4 an F. Habib
43 Pecision of Bundle Block djustent P z Z X = * Z / c Y = * Z / c X Y Z X Y Z c Z c Y X E 59700: Digital Photogaetic Sstes 4 an F. Habib
44 Pecision of Bundle Block djustent Vetical Pecision Flight Diection -ais B c a a a H P = - P / B = c / H H = B c / P E 59700: Digital Photogaetic Sstes 44 an F. Habib
45 Pecision of Bundle Block djustent Vetical Pecision Z Z c Z B p B c Z E 59700: Digital Photogaetic Sstes 45 an F. Habib
46 dvantages of Bundle Block djustent Most accuate tiangulation technique since we have diect tansfoation between iage and gound coodinates. Staight fowad to include paaetes that copensate fo vaious deviations fo the collineait odel. Staight fowad to include additional obsevations: GPS/IS obsevations at the eposue stations Object space distances an be used fo noal, convegent, aeial, and close ange iage fte the adjustent, the EOPs can be set on analog and analtical plottes as well as digital photogaetic wokstations fo copilation puposes. E 59700: Digital Photogaetic Sstes 4 an F. Habib
47 Photogaetic opilation E 59700: Digital Photogaetic Sstes 47 an F. Habib
48 Disadvantages of Bundle Block djustent Model is non linea: appoiations as well as patial deivatives ae needed. Requies copute intensive coputations nalog instuents cannot be used (the cannot easue iage coodinate easueents). he adjustent cannot be sepaated into planietic and vetical adjustent. E 59700: Digital Photogaetic Sstes 48 an F. Habib
49 Bundle djustent: Final Reaks Eleenta Unit: Iages Measueents: Iage coodinates Matheatical odel: ollineait equations Instuents: opaatos, analtical plottes, and Digital Photogaetic Wokstations (DPW) Requied copute powe: Ve lage Epected accuac: High E 59700: Digital Photogaetic Sstes 49 an F. Habib
50 Special ases Resection Intesection Steeo-pai oientation Relative oientation (Discussed in hapte 8) Dependent Relative Oientation (DRO), and Independent Relative Oientation E 59700: Digital Photogaetic Sstes 50 an F. Habib
51 Resection We ae dealing with one iage. We would like to deteine the EOPs of this iage using GPs. Q: What is the iniu GP equieents? t least non-collinea GPs ae equied to estiate the EOPs. t least 5 non-collinea (well distibuted in -D) GPs ae equied to estiate the EOPs and the IOPs ( p, p, c). itical suface: he GPs and the pespective cente lie on a coon clinde. E 59700: Digital Photogaetic Sstes 5 an F. Habib
52 Resection eteio oientation inteio oientation E 59700: Digital Photogaetic Sstes 5 an F. Habib
53 Resection - itical Suface Question: Which paaete of the EOPs cannot be deteined? E 59700: Digital Photogaetic Sstes 5 an F. Habib
54 Intesection We ae dealing with two iages. he EOPs of these iages ae available. he IOPs of the involved caea(s) ae also available. We want to estiate the gound coodinates of tie points in the ovelap aea. Fo each tie point, we have: 4 Obsevation equations Unknowns Redundanc = on-linea odel: appoiations ae needed E 59700: Digital Photogaetic Sstes 54 an F. Habib
55 Intesection a a P P Object Point () E 59700: Digital Photogaetic Sstes 55 an F. Habib
56 Intesection: Linea Model O l B O V l V X Y Z E 59700: Digital Photogaetic Sstes 5 an F. Habib
57 E 59700: Digital Photogaetic Sstes an F. Habib 57 Intesection: Linea Model c R V c R V Z Z Y Y X X B p p p l p l l O O O O O O l l l l l l ),, ( ),, ( hese vectos ae given w..t. the gound coodinate sste.
58 E 59700: Digital Photogaetic Sstes an F. Habib 58 Intesection: Linea Model c R c R Z Z Y Y X X V B V p p p l p l o o o o o o l l l l l l l ),, ( ),, ( hee equations in two unknowns (). he ae linea equations.
59 E 59700: Digital Photogaetic Sstes an F. Habib 59 Intesection: Linea Model c R Z Y X Z Y X p l p l O O O l l l l l l ),, ( c R Z Y X Z Y X p p O O O ),, ( O:
60 Given: Steeo-pai Oientation Steeo-pai: two iages with at least 50% ovelap Iage coodinates of soe tie points Iage and gound coodinates of contol points Requied: he gound coodinates of the tie points he EOPs of the involved iages Mini-Bundle djustent Pocedue E 59700: Digital Photogaetic Sstes 0 an F. Habib
61 Eaple: Given: Steeo-pai Oientation Steeo-pai 0 tie points o gound contol points Question: an we estiate the gound coodinates of the tie points as well as the eteio oientation paaetes of that steeo-pai? nswe: O E 59700: Digital Photogaetic Sstes an F. Habib
62 Sua Photogaet: Definition and applications Photogaetic tools: Rotation atices Photogaetic oientation: inteio and eteio oientation ollineait equations/conditions Photogaetic bundle adjustent Stuctue of the design and noal atices Special cases: Resection, intesection, and steeo-pai oientation E 59700: Digital Photogaetic Sstes an F. Habib
The geometric construction of Ewald sphere and Bragg condition:
The geometic constuction of Ewald sphee and Bagg condition: The constuction of Ewald sphee must be done such that the Bagg condition is satisfied. This can be done as follows: i) Daw a wave vecto k in
30 The Electric Field Due to a Continuous Distribution of Charge on a Line
hapte 0 The Electic Field Due to a ontinuous Distibution of hage on a Line 0 The Electic Field Due to a ontinuous Distibution of hage on a Line Evey integal ust include a diffeential (such as d, dt, dq,
Optimum Settings of Process Mean, Economic Order Quantity, and Commission Fee
Jounal of Applied Science and Engineeing, Vol. 15, No. 4, pp. 343 352 (2012 343 Optiu Settings of Pocess Mean, Econoic Ode Quantity, and Coission Fee Chung-Ho Chen 1 *, Chao-Yu Chou 2 and Wei-Chen Lee
2 Governing Equations
2 Govening Equations This chapte develops the govening equations of motion fo a homogeneous isotopic elastic solid, using the linea thee-dimensional theoy of elasticity in cylindical coodinates. At fist,
Rigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018
Rigid Body Dynamics 2 CSE169: Compute Animation nstucto: Steve Rotenbeg UCSD, Winte 2018 Coss Poduct & Hat Opeato Deivative of a Rotating Vecto Let s say that vecto is otating aound the oigin, maintaining
Chapter 5 Force and Motion
Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to
ATMO 551a Fall 08. Diffusion
Diffusion Diffusion is a net tanspot of olecules o enegy o oentu o fo a egion of highe concentation to one of lowe concentation by ando olecula) otion. We will look at diffusion in gases. Mean fee path
r ˆr F = Section 2: Newton s Law of Gravitation m 2 m 1 Consider two masses and, separated by distance Gravitational force on due to is
Section : Newton s Law of Gavitation In 1686 Isaac Newton published his Univesal Law of Gavitation. This explained avity as a foce of attaction between all atte in the Univese, causin e.. apples to fall
Chapter 5 Force and Motion
Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights
7.2. Coulomb s Law. The Electric Force
Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat
2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum
2. Electostatics D. Rakhesh Singh Kshetimayum 1 2.1 Intoduction In this chapte, we will study how to find the electostatic fields fo vaious cases? fo symmetic known chage distibution fo un-symmetic known
Stress, Cauchy s equation and the Navier-Stokes equations
Chapte 3 Stess, Cauchy s equation and the Navie-Stokes equations 3. The concept of taction/stess Conside the volume of fluid shown in the left half of Fig. 3.. The volume of fluid is subjected to distibuted
Game Study of the Closed-loop Supply Chain with Random Yield and Random Demand
, pp.105-110 http://dx.doi.og/10.14257/astl.2014.53.24 Gae Study of the Closed-loop Supply Chain with ando Yield and ando Deand Xiuping Han, Dongyan Chen, Dehui Chen, Ling Hou School of anageent, Habin
Alignment of the ZEUS Micro- Vertex Detector Using Cosmic Tracks
Alignment of the ZEUS Mico- Vetex etecto Using Cosmic acks akanoi Kohno (Univesity of Oxfod), ZEUS MV Goup Intenational Wokshop on Advanced Computing and Analysis echniques in Physics Reseach (ACA5) ESY,
Research Design - - Topic 9 Fundamentals of Bivariate Regression and Correlation 2010 R. C. Gardner, Ph.D. Bivariate Regression and Correlation.
Reseach Design - - Topic Fundaentals of Bivaiate Regession and Coelation 00 R. C. Gadne, Ph.D. Bivaiate egession - - defining foulae Bivaiate coelation - - defining foulae Test of significance fo egession
Electrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
Adsorption and Desorption Kinetics for Diffusion Controlled Systems with a Strongly Concentration Dependent Diffusivity
The Open-Access Jounal fo the Basic Pinciples of Diffusion Theoy, Expeient and Application Adsoption and Desoption Kinetics fo Diffusion Contolled Systes with a Stongly Concentation Dependent Diffusivity
EN40: Dynamics and Vibrations. Midterm Examination Tuesday March
EN4: Dynaics and Vibations Midte Exaination Tuesday Mach 8 16 School of Engineeing Bown Univesity NME: Geneal Instuctions No collaboation of any kind is peitted on this exaination. You ay bing double sided
VLSI IMPLEMENTATION OF PARALLEL- SERIAL LMS ADAPTIVE FILTERS
VLSI IMPLEMENTATION OF PARALLEL- SERIAL LMS ADAPTIVE FILTERS Run-Bo Fu, Paul Fotie Dept. of Electical and Copute Engineeing, Laval Univesity Québec, Québec, Canada GK 7P4 eail: fotie@gel.ulaval.ca Abstact
LECTURE 15. Phase-amplitude variables. Non-linear transverse motion
LETURE 5 Non-linea tansvese otion Phase-aplitude vaiables Second ode (quadupole-diven) linea esonances Thid-ode (sextupole-diven) non-linea esonances // USPAS Lectue 5 Phase-aplitude vaiables Although
Look over Chapter 22 sections 1-8 Examples 2, 4, 5, Look over Chapter 16 sections 7-9 examples 6, 7, 8, 9. Things To Know 1/22/2008 PHYS 2212
PHYS 1 Look ove Chapte sections 1-8 xamples, 4, 5, PHYS 111 Look ove Chapte 16 sections 7-9 examples 6, 7, 8, 9 Things To Know 1) What is an lectic field. ) How to calculate the electic field fo a point
(n 1)n(n + 1)(n + 2) + 1 = (n 1)(n + 2)n(n + 1) + 1 = ( (n 2 + n 1) 1 )( (n 2 + n 1) + 1 ) + 1 = (n 2 + n 1) 2.
Paabola Volume 5, Issue (017) Solutions 151 1540 Q151 Take any fou consecutive whole numbes, multiply them togethe and add 1. Make a conjectue and pove it! The esulting numbe can, fo instance, be expessed
(A) 2log( tan cot ) [ ], 2 MATHEMATICS. 1. Which of the following is correct?
![(A) 2log( tan cot ) [ ], 2 MATHEMATICS. 1. Which of the following is correct?](/thumbs/76/73747145.jpg "(A) 2log( tan cot ) [ ], 2 MATHEMATICS. 1. Which of the following is correct?")
MATHEMATICS. Which of the following is coect? A L.P.P always has unique solution Evey L.P.P has an optimal solution A L.P.P admits two optimal solutions If a L.P.P admits two optimal solutions then it
Tutorial on Strehl ratio, wavefront power series expansion, Zernike polynomials expansion in small aberrated optical systems By Sheng Yuan
Tutoial on Stel atio, wavefont powe seies expansion, Zenike polynomials expansion in small abeated optical systems By Seng Yuan. Stel Ratio Te wave abeation function, (x,y, is defined as te distance, in
Tidal forces. m r. m 1 m 2. x r 2. r 1
Tidal foces Befoe we look at fee waves on the eath, let s fist exaine one class of otion that is diectly foced: astonoic tides. Hee we will biefly conside soe of the tidal geneating foces fo -body systes.
Chapter 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
Physics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
Light Time Delay and Apparent Position
Light Time Delay and ppaent Position nalytical Gaphics, Inc. www.agi.com info@agi.com 610.981.8000 800.220.4785 Contents Intoduction... 3 Computing Light Time Delay... 3 Tansmission fom to... 4 Reception
SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9
SPH4 nit 6.3 Gavitational Potential negy Page of Notes Physics ool box he gavitational potential enegy of a syste of two (spheical) asses is diectly popotional to the poduct of thei asses, and invesely
Physics Courseware Electromagnetism
Pysics Cousewae lectomagnetism lectic field Poblem.- a) Find te electic field at point P poduced by te wie sown in te figue. Conside tat te wie as a unifom linea cage distibution of λ.5µ C / m b) Find
1121 T Question 1
1121 T1 2008 Question 1 ( aks) You ae cycling, on a long staight path, at a constant speed of 6.0.s 1. Anothe cyclist passes you, tavelling on the sae path in the sae diection as you, at a constant speed
Video Geometry without Shape
Video Geoety without Shape Retieving geoetical infoation in videos without any a pioi infoation about the iage stuctue o possible shapes: Taás Sziányi Registation of diffeent views, o io, o shadows though
Section 26 The Laws of Rotational Motion
Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to
t is bounded. Thus, the state derivative x t is bounded. Let y Cx represent the system output. Then y
Lectue 3 Eaple 6.3 Conside an LI syste A Bu with a Huwitz ati A and a unifoly ounded in tie input ut. hese two facts iply that the state t is ounded. hus, the state deivative t is ounded. Let y C epesent
3.6 Applied Optimization
.6 Applied Optimization Section.6 Notes Page In this section we will be looking at wod poblems whee it asks us to maimize o minimize something. Fo all the poblems in this section you will be taking the
Lab #9: The Kinematics & Dynamics of. Circular Motion & Rotational Motion
Reading Assignment: Lab #9: The Kinematics & Dynamics of Cicula Motion & Rotational Motion Chapte 6 Section 4 Chapte 11 Section 1 though Section 5 Intoduction: When discussing motion, it is impotant to
Cartesian Control. Analytical inverse kinematics can be difficult to derive Inverse kinematics are not as well suited for small differential motions
Catesian Contol Analtical invese kinematics can e diicult to deive Invese kinematics ae not as well suited o small dieential motions Let s take a look at how ou use the acoian to contol Catesian position
Newton s Laws, Kepler s Laws, and Planetary Orbits
Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion
COLLAPSING WALLS THEOREM
COLLAPSING WALLS THEOREM IGOR PAK AND ROM PINCHASI Abstact. Let P R 3 be a pyamid with the base a convex polygon Q. We show that when othe faces ae collapsed (otated aound the edges onto the plane spanned
Electromagnetic scattering. Graduate Course Electrical Engineering (Communications) 1 st Semester, Sharif University of Technology
Electomagnetic scatteing Gaduate Couse Electical Engineeing (Communications) 1 st Semeste, 1390-1391 Shaif Univesity of Technology Geneal infomation Infomation about the instucto: Instucto: Behzad Rejaei
Lecture 8 - Gauss s Law
Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.
Chapter. s r. check whether your calculator is in all other parts of the body. When a rigid body rotates through a given angle, all
conveted to adians. Also, be sue to vanced to a new position (Fig. 7.2b). In this inteval, the line OP has moved check whethe you calculato is in all othe pats of the body. When a igid body otates though
Black Body Radiation and Radiometric Parameters:
Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo
A New I 1 -Based Hyperelastic Model for Rubber Elastic Materials
A New I -Based Hypeelastic Model fo Rubbe Elastic Mateials Osca Lopez-Paies SES Octobe -4, Evanston, IL Neo-Hookean odel W ìï ï ( I - ) = ( if l + l + l - ) lll = = í ï + othewise ïî (*). Matheatical siplicity
1 Spherical multipole moments
Jackson notes 9 Spheical multipole moments Suppose we have a chage distibution ρ (x) wheeallofthechageiscontained within a spheical egion of adius R, as shown in the diagam. Then thee is no chage in the
Analytic Evaluation of two-electron Atomic Integrals involving Extended Hylleraas-CI functions with STO basis
Analytic Evaluation of two-electon Atomic Integals involving Extended Hylleaas-CI functions with STO basis B PADHY (Retd.) Faculty Membe Depatment of Physics, Khalikote (Autonomous) College, Behampu-760001,
Δt The textbook chooses to say that the average velocity is
1-D Motion Basic I Definitions: One dimensional motion (staight line) is a special case of motion whee all but one vecto component is zeo We will aange ou coodinate axis so that the x-axis lies along the
Chapter 4. Newton s Laws of Motion
Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto
Capacitance Extraction. Classification (orthogonal to 3D/2D)
Capacitance Etaction n Intoduction n Table lookup metod n Fomula-based metod n Numeical metod Classification otogonal to D/D n Numeical metod accuate an geometic stuctues etemel epensive n Fomula-based
The condition for maximum intensity by the transmitted light in a plane parallel air film is. For an air film, μ = 1. (2-1)
hapte Two Faby--Peot ntefeomete A Faby-Peot intefeomete consists of two plane paallel glass plates A and B, sepaated by a distance d. The inne sufaces of these plates ae optically plane and thinly silveed
COUPLED MODELS OF ROLLING, SLIDING AND WHIRLING FRICTION
ENOC 008 Saint Petesbug Russia June 30-July 4 008 COUPLED MODELS OF ROLLING SLIDING AND WHIRLING FRICTION Alexey Kieenkov Ins ti tu te fo P ob le ms in Me ch an ic s Ru ss ia n Ac ad em y of Sc ie nc es
Vortex Initialization in HWRF/HMON Models
Votex Initialization in HWRF/HMON Models HWRF Tutoial Januay 018 Pesented by Qingfu Liu NOAA/NCEP/EMC 1 Outline 1. Oveview. HWRF cycling syste 3. Bogus sto 4. Sto elocation 5. Sto size coection 6. Sto
Physics 11 Chapter 3: Vectors and Motion in Two Dimensions. Problem Solving
Physics 11 Chapte 3: Vectos and Motion in Two Dimensions The only thing in life that is achieved without effot is failue. Souce unknown "We ae what we epeatedly do. Excellence, theefoe, is not an act,
Relative motion (Translating axes)
Relative motion (Tanslating axes) Paticle to be studied This topic Moving obseve (Refeence) Fome study Obseve (no motion) bsolute motion Relative motion If motion of the efeence is known, absolute motion
$ i. !((( dv vol. Physics 8.02 Quiz One Equations Fall q 1 q 2 r 2 C = 2 C! V 2 = Q 2 2C F = 4!" or. r ˆ = points from source q to observer
Physics 8.0 Quiz One Equations Fall 006 F = 1 4" o q 1 q = q q ˆ 3 4" o = E 4" o ˆ = points fom souce q to obseve 1 dq E = # ˆ 4" 0 V "## E "d A = Q inside closed suface o d A points fom inside to V =
221B Lecture Notes Scattering Theory I
Why Scatteing? B Lectue Notes Scatteing Theoy I Scatteing of paticles off taget has been one of the most impotant applications of quantum mechanics. It is pobably the most effective way to study the stuctue
Three dimensional flow analysis in Axial Flow Compressors
1 Thee dimensional flow analysis in Axial Flow Compessos 2 The ealie assumption on blade flow theoies that the flow inside the axial flow compesso annulus is two dimensional means that adial movement of
Centripetal Force OBJECTIVE INTRODUCTION APPARATUS THEORY
Centipetal Foce OBJECTIVE To veify that a mass moving in cicula motion expeiences a foce diected towad the cente of its cicula path. To detemine how the mass, velocity, and adius affect a paticle's centipetal
Study on GPS Common-view Observation Data with Multiscale Kalman Filter. based on correlation Structure of the Discrete Wavelet Coefficients
Study on GPS Coon-view Obsevation Data with ultiscale Kalan Filte based on coelation Stuctue of the Discete Wavelet Coefficients Ou Xiaouan Zhou Wei Yu Jianguo Dept. of easueent and Instuentation, Xi dian
Phys 201A. Homework 5 Solutions
Phys 201A Homewok 5 Solutions 3. In each of the thee cases, you can find the changes in the velocity vectos by adding the second vecto to the additive invese of the fist and dawing the esultant, and by
Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E)
Geneal physics II (10) D. Iyad D. Iyad Chapte : lectic Fields In this chapte we will cove The lectic Field lectic Field Lines -: The lectic Field () lectic field exists in a egion of space suounding a
Math 2263 Solutions for Spring 2003 Final Exam
Math 6 Solutions fo Sping Final Exam ) A staightfowad appoach to finding the tangent plane to a suface at a point ( x, y, z ) would be to expess the cuve as an explicit function z = f ( x, y ), calculate
B. Spherical Wave Propagation
11/8/007 Spheical Wave Popagation notes 1/1 B. Spheical Wave Popagation Evey antenna launches a spheical wave, thus its powe density educes as a function of 1, whee is the distance fom the antenna. We
Physics 11 Chapter 4: Forces and Newton s Laws of Motion. Problem Solving
Physics 11 Chapte 4: Foces and Newton s Laws of Motion Thee is nothing eithe good o bad, but thinking makes it so. William Shakespeae It s not what happens to you that detemines how fa you will go in life;
Center of Mass and Linear
PH 22-3A Fall 2009 Cente of Mass and Linea Moentu Lectue 5 Chapte 8 (Halliday/Resnick/Walke, Fundaentals of Physics 8 th edition) Chapte 9 Cente of Mass and Linea Moentu In this chapte we will intoduce
2-Monoid of Observables on String G
2-Monoid of Obsevables on Sting G Scheibe Novembe 28, 2006 Abstact Given any 2-goupoid, we can associate to it a monoidal categoy which can be thought of as the 2-monoid of obsevables of the 2-paticle
Review: Electrostatics and Magnetostatics
Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion
Levitation force analysis of ring and disk shaped permanent magnet-high temperature superconductor
Inn Jounal of Pue & Applied Physics Vol. 55, Apil 017, pp. 61-68 Levitation foce analysis of ing and disk shaped pemanent magnet-high tempeatue supeconducto Sinan Basaan & Selim Sivioglu* Depatment of
Chapter 2: Introduction to Implicit Equations
Habeman MTH 11 Section V: Paametic and Implicit Equations Chapte : Intoduction to Implicit Equations When we descibe cuves on the coodinate plane with algebaic equations, we can define the elationship
Some Remarks on the Boundary Behaviors of the Hardy Spaces
Soe Reaks on the Bounday Behavios of the Hady Spaces Tao Qian and Jinxun Wang In eoy of Jaie Kelle Abstact. Soe estiates and bounday popeties fo functions in the Hady spaces ae given. Matheatics Subject
A Relativistic Electron in a Coulomb Potential
A Relativistic Electon in a Coulomb Potential Alfed Whitehead Physics 518, Fall 009 The Poblem Solve the Diac Equation fo an electon in a Coulomb potential. Identify the conseved quantum numbes. Specify
2. Plane Elasticity Problems
S0 Solid Mechanics Fall 009. Plane lasticity Poblems Main Refeence: Theoy of lasticity by S.P. Timoshenko and J.N. Goodie McGaw-Hill New Yok. Chaptes 3..1 The plane-stess poblem A thin sheet of an isotopic
Chapter 1: Introduction to Polar Coordinates
Habeman MTH Section III: ola Coodinates and Comple Numbes Chapte : Intoduction to ola Coodinates We ae all comfotable using ectangula (i.e., Catesian coodinates to descibe points on the plane. Fo eample,
Question Bank. Section A. is skew-hermitian matrix. is diagonalizable. (, ) , Evaluate (, ) 12 about = 1 and = Find, if
Subject: Mathematics-I Question Bank Section A T T. Find the value of fo which the matix A = T T has ank one. T T i. Is the matix A = i is skew-hemitian matix. i. alculate the invese of the matix = 5 7
MAGNETIC FIELD AROUND TWO SEPARATED MAGNETIZING COILS
The 8 th Intenational Confeence of the Slovenian Society fo Non-Destuctive Testing»pplication of Contempoay Non-Destuctive Testing in Engineeing«Septembe 1-3, 5, Potoož, Slovenia, pp. 17-1 MGNETIC FIELD
Uniform Circular Motion
Unifom Cicula Motion Intoduction Ealie we defined acceleation as being the change in velocity with time: a = v t Until now we have only talked about changes in the magnitude of the acceleation: the speeding
Chapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
SIO 229 Gravity and Geomagnetism. Lecture 6. J 2 for Earth. J 2 in the solar system. A first look at the geoid.
SIO 229 Gavity and Geomagnetism Lectue 6. J 2 fo Eath. J 2 in the sola system. A fist look at the geoid. The Thee Big Themes of the Gavity Lectues 1.) An ellipsoidal otating Eath Refeence body (mass +
Physics 2B Chapter 22 Notes - Magnetic Field Spring 2018
Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field
Homework # 3 Solution Key
PHYSICS 631: Geneal Relativity Homewok # 3 Solution Key 1. You e on you hono not to do this one by hand. I ealize you can use a compute o simply look it up. Please don t. In a flat space, the metic in
PROBLEM SET #1 SOLUTIONS by Robert A. DiStasio Jr.
POBLM S # SOLUIONS by obet A. DiStasio J. Q. he Bon-Oppenheime appoximation is the standad way of appoximating the gound state of a molecula system. Wite down the conditions that detemine the tonic and
Equations to Calculate Characteristic Frequencies of Multiple Chamber Aligned in Parallel Cavity Resonator (MCAP-CR)
MCAPE Equations to Calculate Chaacteistic Fequencies of Multiple Chabe Aligne in Paallel Cavity Resonato (MCAP-CR) Shigeu Suzui Mach, (Revise in ovebe, ). Peface It is necessay to solve the equations of
Brief summary of functional analysis APPM 5440 Fall 2014 Applied Analysis
Bief summay of functional analysis APPM 5440 Fall 014 Applied Analysis Stephen Becke, stephen.becke@coloado.edu Standad theoems. When necessay, I used Royden s and Keyzsig s books as a efeence. Vesion
MCV4U Final Exam Review. 1. Consider the function f (x) Find: f) lim. a) lim. c) lim. d) lim. 3. Consider the function: 4. Evaluate. lim. 5. Evaluate.
MCVU Final Eam Review Answe (o Solution) Pactice Questions Conside the function f () defined b the following gaph Find a) f ( ) c) f ( ) f ( ) d) f ( ) Evaluate the following its a) ( ) c) sin d) π / π
Phys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1
Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the
Handout: IS/LM Model
Econ 32 - IS/L odel Notes Handout: IS/L odel IS Cuve Deivation Figue 4-4 in the textbook explains one deivation of the IS cuve. This deivation uses the Induced Savings Function fom Chapte 3. Hee, I descibe
(r) = 1. Example: Electric Potential Energy. Summary. Potential due to a Group of Point Charges 9/10/12 1 R V(r) + + V(r) kq. Chapter 23.
Eample: Electic Potential Enegy What is the change in electical potential enegy of a eleased electon in the atmosphee when the electostatic foce fom the nea Eath s electic field (diected downwad) causes
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department. Problem Set 10 Solutions. r s
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Depatment Physics 8.033 Decembe 5, 003 Poblem Set 10 Solutions Poblem 1 M s y x test paticle The figue above depicts the geomety of the poblem. The position
Chapter Sixteen: Electric Charge and Electric Fields
Chapte Sixteen: Electic Chage and Electic Fields Key Tems Chage Conducto The fundamental electical popety to which the mutual attactions o epulsions between electons and potons ae attibuted. Any mateial
Euclidean Figures and Solids without Incircles or Inspheres
Foum Geometicoum Volume 16 (2016) 291 298. FOUM GEOM ISSN 1534-1178 Euclidean Figues and Solids without Incicles o Insphees Dimitis M. Chistodoulou bstact. ll classical convex plana Euclidean figues that
In many engineering and other applications, the. variable) will often depend on several other quantities (independent variables).
II PARTIAL DIFFERENTIATION FUNCTIONS OF SEVERAL VARIABLES In man engineeing and othe applications, the behaviou o a cetain quantit dependent vaiable will oten depend on seveal othe quantities independent
Physics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 6: motion in two and three dimensions III. Slide 6-1
Physics 1501 Fall 2008 Mechanics, Themodynamics, Waves, Fluids Lectue 6: motion in two and thee dimensions III Slide 6-1 Recap: elative motion An object moves with velocity v elative to one fame of efeence.
Our Universe: GRAVITATION
Ou Univese: GRAVITATION Fom Ancient times many scientists had shown geat inteest towads the sky. Most of the scientist studied the motion of celestial bodies. One of the most influential geek astonomes
Chapter 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
Electromagnetic Waves
Chapte 32 Electomagnetic Waves PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified P. Lam 8_11_2008 Topics fo Chapte 32 Maxwell s equations
Interpretation Of Wind Components As Compositional Variables
Intepetation Of Wind Coponents As Copositional Vaiables Pablo Buenestado-Caballeo, Eusebi Jaauta-Bagulat, Cae Heada-ala Depataent de Mateàtica Aplicada III, Escola Uniesitàia Engineia Tècnica Industial
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
Radial Inflow Experiment:GFD III
Radial Inflow Expeiment:GFD III John Mashall Febuay 6, 003 Abstact We otate a cylinde about its vetical axis: the cylinde has a cicula dain hole in the cente of its bottom. Wate entes at a constant ate
PHYS 1114, Lecture 21, March 6 Contents:
PHYS 1114, Lectue 21, Mach 6 Contents: 1 This class is o cially cancelled, being eplaced by the common exam Tuesday, Mach 7, 5:30 PM. A eview and Q&A session is scheduled instead duing class time. 2 Exam
#7A&B Magnetic force between two conductors
#7A& Magnetic foce between two conductos This expeiment will be done duing two lab sessions. n the fist we become familia with the appaatus and make one set of measuements. n the second session, we complete