ANNEXE C Modèle mathématique du robot lego NXT
|
|
|
- Rosa Day
- 6 years ago
- Views:
Transcription
1 ANNEXE C Modèe athéatique du oot ego NX tié de a otice NXay-GS Mode-Based Desig - Coto of sef-aacig to-heeed oot uit ith LEGO Midstos NX, Yoihisa Yaaoto.
2 3 NXay-GS Modeig his chapte descies atheatica ode ad otio equatios of NXay-GS. 3. o-heeed Iveted Peduu Mode NXay-GS ca e cosideed as a to heeed iveted peduu ode sho i igue 3-. D H igue 3- o-heeed iveted peduu igue 3- shos side vie ad pae vie of the to heeed iveted peduu. he coodiate syste used i 3. Motio Equatios of o-heeed Iveted Peduu is descied i igue 3-. z y z M, L H y y, y, y z, x x x x x : ody pitch age : hee age ( idicates eft ad ight,,, : DC oto age igue 3- Side vie ad pae vie of to-heeed iveted peduu - 6 -
3 Physica paaetes of NXay-GS ae the fooig. g 9.8 [ / sec ] 0.03 [kg] 0.04 [] : Gavity acceeatio : hee eight : hee adius [ kg ] : hee ietia oet M 0.6 [kg] 0.4 [] D 0.04 [] H 0.44 [] : Body eight : Body idth : Body depth : Body height L H [] : Distace of the cete of ass fo the hee axe ML 3 [ kg ] : Body pitch ietia oet ( D M [ kg ] : Body ya ietia oet 5 0 [ kg ] 6.69 [Ω] : DC oto ietia oet : DC oto esistace K [ V sec ad ] : DC oto ack EM costat K 0.37 [ N A] : DC oto toque costat t : Gea atio f 0.00 : ictio coefficiet etee ody ad DC oto f 0 : ictio coefficiet etee hee ad foo. e use the vaues descied i efeece [] fo, K, K. e use the vaues that sees to e appopiate fo,, f, f, ecause it is difficut to easue. t 3. Motio Equatios of o-heeed Iveted Peduu e ca deive otio equatios of to-heeed iveted peduu y the Lagagia ethod ased o the coodiate syste i igue 3-. If the diectio of to-heeed iveted peduu is x-axis positive diectio at t 0, each coodiates ae give as the fooig., (3. ( ( ( ( x y, z ( x dt, y dt, ( x, y ( cos si,, ( x, y, z x si, y cos, z ( x, y, z x si, y cos, z (3. (3.3 (3.4 ( x, y, z ( x Lsi cos, y Lsi si, z Lcos (
4 he tasatioa kietic eegy, the otatioa kietic eegy, the potetia eegy U ae ( y z ( x y z M ( x y z x (3.6 ( ( (3.7 U gz gz Mgz (3.8 he fifth ad sixth te i Lagagia L has the fooig expessio. ae otatio kietic eegy of a aatue i eft ad ight DC oto. he L U (3.9 e use the fooig vaiaes as the geeaized coodiates. : Aveage age of eft ad ight hee : Body pitch age : Body ya age Lagage equatios ae the fooig d dt d dt d dt L L L L L L (3.0 (3. (3. e deive the fooig equatios y evauatig Eqs. (3.0 - (3.. [( M ] ( ML cos ML si (3.3 ( ML cos ( ML MgL si ML si cos (3.4 ( ML si ML si cos (
5 I cosideatio of DC oto toque ad viscous fictio, the geeaized foces ae give as the fooig (,,, (, (3.6 K ti f ( f (3.7 K ti f ( f (3.8 K i K i f f ( (3.9 t t ( hee i, is the DC oto cuet. e caot use the DC oto cuet diecty i ode to coto it ecause it is ased o PM (votage coto. heefoe, e evauate the eatio etee cuet ad votage usig DC oto equatio. If the fictio iside the oto is egigie, the DC oto equatio is geeay as foos i, v, L i, v, K (, i, (3.0 Hee e coside that the oto iductace is egigie ad is appoxiated as zeo. heefoe the cuet is i, v, K (, (3. o Eq.(3., the geeaized foce ca e expessed usig the oto votage. ( v ( v f ( v v (3. (3.3 f K ( v v ( K K (3.4 t t, f (
6 State Equatios of o-heeed Iveted Peduu e ca deive state equatios ased o ode coto theoy y ieaizig otio equatios at a aace poit of NXay-GS. It eas that e coside the iit 0 ( si, cos ad egect the secod ode te ike. he otio equatios (3.3 (3.5 ae appoxiated as the fooig ( [ ] ( ML M (3.6 ( ( MgL ML ML (3.7 ( (3.8 Eq. (3.6 ad Eq. (3.7 has ad, Eq. (3.8 has oy. hese equatios ca e expessed i the fo v v H G E (3.9 ( H MgL G f ML ML ML M E ( v v K I (3.30 ( ( K f I
7 Hee e coside the fooig vaiaes x, as state, ad u as iput. x idicates taspose of x. x [,,, ], x [, ], [ v, v ] u (3.3 x Cosequety, e ca deive state equatios of to-heeed iveted peduu fo Eq. (3.9 ad Eq. (3.30. A x u (3.3 x B A x u (3.33 x B A , B ( A (3, (3,3 (3,4 (3 (3 A A B B 0 A (4, A (4,3 A (4,4 B (4 B (4 A 0 0, I B 0 K 0 I K I (3.35 A (3, gmle(, det( E A (4, gmle(, det( E A (3,3 A (4,3 A (3,4 A (4,4 B (3 B (4 [ ( f E(, E(, ] [ ( f E(, E(, ] [ E(, E(, ] det( E [ E(, E(, ] det( E [ E(, E(, ] det( E [ E(, E(, ] det( E det( E E(, E(, E(, det( E det( E - -
Quantum Mechanics Lecture Notes 10 April 2007 Meg Noah
The -Patice syste: ˆ H V This is difficut to sove. y V 1 ˆ H V 1 1 1 1 ˆ = ad with 1 1 Hˆ Cete of Mass ˆ fo Patice i fee space He Reative Haitoia eative coodiate of the tota oetu Pˆ the tota oetu tota
Ground Rules. PC1221 Fundamentals of Physics I. Uniform Circular Motion, cont. Uniform Circular Motion (on Horizon Plane) Lectures 11 and 12
PC11 Fudametals of Physics I Lectues 11 ad 1 Cicula Motio ad Othe Applicatios of Newto s Laws D Tay Seg Chua 1 Goud Rules Switch off you hadphoe ad page Switch off you laptop compute ad keep it No talkig
CHAPTER 5 : SERIES. 5.2 The Sum of a Series Sum of Power of n Positive Integers Sum of Series of Partial Fraction Difference Method
CHAPTER 5 : SERIES 5.1 Seies 5. The Sum of a Seies 5..1 Sum of Powe of Positive Iteges 5.. Sum of Seies of Patial Factio 5..3 Diffeece Method 5.3 Test of covegece 5.3.1 Divegece Test 5.3. Itegal Test 5.3.3
Masses and orbits of minor planets with the GAIA mission
asses ad obits of io laets with the GAIA issio Sege ouet Suevisos : F.igad D.Hestoffe PLAN Itoductio Puose of the PhD Iotace of asses The diffeet ethods to estiate these asses Descitio of close aoach Diffeet
Technical Report: Bessel Filter Analysis
Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we
VIII Dynamics of Systems of Particles
VIII Dyacs of Systes of Patcles Cete of ass: Cete of ass Lea oetu of a Syste Agula oetu of a syste Ketc & Potetal Eegy of a Syste oto of Two Iteactg Bodes: The Reduced ass Collsos: o Elastc Collsos R whee:
rad / sec min rev 60sec. 2* rad / sec s
EE 559, Exa 2, Spig 26, D. McCalley, 75 iute allowed. Cloed Book, Cloed Note, Calculato Peitted, No Couicatio Device. (6 pt) Coide a.5 MW, 69 v, 5 Hz, 75 p DFG wid eegy yt. he paaete o the geeato ae give
Multivector Functions
I: J. Math. Aal. ad Appl., ol. 24, No. 3, c Academic Pess (968) 467 473. Multivecto Fuctios David Hestees I a pevious pape [], the fudametals of diffeetial ad itegal calculus o Euclidea -space wee expessed
CHAPTER 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
W = mgdz = mgh. We can express this potential as a function of z: V ( z) = gz. = mg k. dz dz
Electoagetic Theoy Pof Ruiz, UNC Asheville, doctophys o YouTube Chapte M Notes Laplace's Equatio M Review of Necessay Foe Mateial The Electic Potetial Recall i you study of echaics the usefuless of the
Self-Consistent Simulations of Beam and Plasma Systems Final Exam ( take-home )
Sef-Cosistet Simuatios of Beam ad Pasma Systems Fia Exam ( take-home ) S. M. Lud, J.-L. Vay, R. Lehe, ad D. Wikeher Thursday, Jue 16 th, 2016 Probem 1 - Maxwe s equatios ad redudat iformatio. a) Show that
physicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jauay 2009 2 a 7. Give that X = 1 1, whee a is a costat, ad a 2, blak (a) fid X 1 i tems of a. Give that X + X 1 = I, whee I is the 2 2 idetity matix, (b)
Physics 161 Fall 2011 Extra Credit 2 Investigating Black Holes - Solutions The Following is Worth 50 Points!!!
Physics 161 Fall 011 Exta Cedit Investigating Black Holes - olutions The Following is Woth 50 Points!!! This exta cedit assignment will investigate vaious popeties of black holes that we didn t have time
KEY. Math 334 Midterm II Fall 2007 section 004 Instructor: Scott Glasgow
KEY Math 334 Midtem II Fall 7 sectio 4 Istucto: Scott Glasgow Please do NOT wite o this exam. No cedit will be give fo such wok. Rathe wite i a blue book, o o you ow pape, pefeably egieeig pape. Wite you
ANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main)
AIITS-HT-VII-PM-JEE(Mai)-Sol./7 I JEE Advaced 06, FIITJEE Studets bag 6 i Top 00 AIR, 7 i Top 00 AIR, 8 i Top 00 AIR. Studets fom Log Tem lassoom/ Itegated School Pogam & Studets fom All Pogams have qualified
a) The average (mean) of the two fractions is halfway between them: b) The answer is yes. Assume without loss of generality that p < r.
Solutios to MAML Olympiad Level 00. Factioated a) The aveage (mea) of the two factios is halfway betwee them: p ps+ q ps+ q + q s qs qs b) The aswe is yes. Assume without loss of geeality that p
BBU Codes Overview. Outline Introduction Beam transport Equation How to solve (BBU-R, TDBBUU, bi, MATBBU etc.) Comparison of BBU codes
BBU Codes Oveview asau Sawamua ad Ryoichi Hajima JAERI Outie Itoductio Beam tasot Equatio How to sove BBU-R, DBBUU, bi, ABBU etc. Comaiso of BBU codes Itoductio ERL cuet imited by Beam Beaku asvese defect
Kinematics, Dynamics & Control
Kiematics, Dyamics & Cotol DH aametes Ais (i-) Ais i Velocity/oce Duality i- i = i- Li i- z i- i- a i- z i a i i Li i i } i c i -s i 0 a i- s i c i- c i c i- -s i- -s i- i s i s i- c i s i- c i- c i- i
Lecture 23: Central Force Motion
Lectue 3: Cental Foce Motion Many of the foces we encounte in natue act between two paticles along the line connecting the Gavity, electicity, and the stong nuclea foce ae exaples These types of foces
ROTATIONAL MOTION PR 1
Eistei Classes, Uit No.,, Vadhma Rig Road Plaza, Vikas Pui Ext., Oute Rig Road New Delhi 8, Ph. : 969, 87 PR ROTATIONAL MOTION Syllabus : Cete of mass of a two-paticles system, Cete of mass of a igid body;
THE GRAVITATIONAL POTENTIAL OF A MULTIDIMENSIONAL SHELL
THE GRAVITATIONAL POTENTIAL OF A MULTIDIMENSIONAL SHELL BY MUGUR B. RĂUŢ Abstact. This pape is a attept to geealize the well-kow expessio of the gavitatioal potetial fo oe tha thee diesios. We used the
Consider two masses m 1 at x = x 1 and m 2 at x 2.
Chapte 09 Syste of Patcles Cete of ass: The cete of ass of a body o a syste of bodes s the pot that oes as f all of the ass ae cocetated thee ad all exteal foces ae appled thee. Note that HRW uses co but
(a) Calculate the apparent weight of the student in the first part of the journey while accelerating downwards at 2.35 m s 2.
Chapte answes Heineann Physics 1 4e Section.1 Woked exaple: Ty youself.1.1 CALCULATING APPARENT WEIGHT A 79.0 kg student ides a lift down fo the top floo of an office block to the gound. Duing the jouney
Lecture 2: Stress. 1. Forces Surface Forces and Body Forces
Lectue : Stess Geophysicists study pheomea such as seismicity, plate tectoics, ad the slow flow of ocks ad mieals called ceep. Oe way they study these pheomea is by ivestigatig the defomatio ad flow of
Reference Guide & Formula Sheet for Physics
D. Hoselto & M. Pice Page of 8 #0 Heatig a Solid, Liquid o Gas #3 Compoets of a Vecto Q = m c T if V = 34 m/sec 48 the V i = 34 m/sec (cos 48 ); ad V J = 34 m/sec (si 48 ) #4 Weight = m g g = 9.8m/sec²
Asymptotic Expansions of Legendre Wavelet
Asptotic Expasios of Legede Wavelet C.P. Pade M.M. Dixit * Depatet of Matheatics NERIST Nijuli Itaaga Idia. Depatet of Matheatics NERIST Nijuli Itaaga Idia. Astact A e costuctio of avelet o the ouded iteval
Engineering Mechanics Dynamics & Vibrations. Engineering Mechanics Dynamics & Vibrations Plane Motion of a Rigid Body: Equations of Motion
1/5/013 Egieerig Mechaics Dyaics ad Vibratios Egieerig Mechaics Dyaics & Vibratios Egieerig Mechaics Dyaics & Vibratios Plae Motio of a Rigid Body: Equatios of Motio Motio of a rigid body i plae otio is
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
HW Solutions # MIT - Prof. Please study example 12.5 "from the earth to the moon". 2GmA v esc
HW Solutions # 11-8.01 MIT - Pof. Kowalski Univesal Gavity. 1) 12.23 Escaping Fom Asteoid Please study example 12.5 "fom the eath to the moon". a) The escape velocity deived in the example (fom enegy consevation)
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
Multi-parameter Analysis of a Rigid Body. Nonlinear Coupled Rotations around
Adv. Theo. Appl. Mech., Vol. 6, 3, o., 9-7 HIKARI Ltd, www.m-hikai.com http://dx.doi.og/.988/atam.3.378 Multi-paamete Aalysis of a Rigid Body Noliea Coupled Rotatios aoud No Itesectig Axes Based o the
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.
- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.
- 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU
Exercises and Problems
HW Chapter 4: Oe-Dimesioal Quatum Mechaics Coceptual Questios 4.. Five. 4.4.. is idepedet of. a b c mu ( E). a b m( ev 5 ev) c m(6 ev ev) Exercises ad Problems 4.. Model: Model the electro as a particle
Latticed pentamode acoustic cloak (supplementary Info)
Lattied petamode aousti loak (supplemetay Ifo) Yi Che, Xiaoig Liu ad Gegkai Hu Key Laboatoy of yamis ad Cotol of Flight Vehile, Miisty of Eduatio, Shool of Aeospae Egieeig, Beiig Istitute of Tehology,
2012 GCE A Level H2 Maths Solution Paper Let x,
GCE A Level H Maths Solutio Pape. Let, y ad z be the cost of a ticet fo ude yeas, betwee ad 5 yeas, ad ove 5 yeas categoies espectively. 9 + y + 4z =. 7 + 5y + z = 8. + 4y + 5z = 58.5 Fo ude, ticet costs
B l 4 P A 1 DYNAMICS OF RECIPROCATING ENGINES
DYNMIS OF REIROTING ENGINES This chapte studies the dnaics of a side cank echaniss in an anatica wa. This is an eape fo the anatica appoach of soution instead of the gaphica acceeations and foce anases.
physicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jue 005. A cuve has equatio blak x + xy 3y + 16 = 0. dy Fid the coodiates of the poits o the cuve whee 0. dx = (7) Q (Total 7 maks) *N03B034* 3 Tu ove physicsadmathstuto.com
Gravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun
Chapte 12 Gavitation PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified by P. Lam 5_31_2012 Goals fo Chapte 12 To study Newton s Law
Universal Gravitation
Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between
Advanced Higher Formula List
Advaced Highe Fomula List Note: o fomulae give i eam emembe eveythig! Uit Biomial Theoem Factoial! ( ) ( ) Biomial Coefficiet C!! ( )! Symmety Idetity Khayyam-Pascal Idetity Biomial Theoem ( y) C y 0 0
TOOTH SURFACE FUNDAMENTAL FORMS IN GEAR TECHNOLOGY UDC:
NIRSIT O NIŠ The scietific joual ACTA NIRSITATIS Seies: Mechaical gieeig ol1 N o 5 1998 pp 515-55 dito of seies: Nead Radojković e-mail: adojkovic@iacyu Addess: ivezitetski tg 18000 Niš Tel: 381 18 547-095
GRAVITATIONAL FORCE IN HYDROGEN ATOM
Fudametal Joual of Mode Physics Vol. 8, Issue, 015, Pages 141-145 Published olie at http://www.fdit.com/ GRAVITATIONAL FORCE IN HYDROGEN ATOM Uiesitas Pedidika Idoesia Jl DR Setyabudhi No. 9 Badug Idoesia
Niraj Sir. circular motion;; SOLUTIONS TO CONCEPTS CHAPTER 7
SOLUIONS O CONCEPS CHAPE 7 cicula otion;;. Distance between Eath & Moon.85 0 5 k.85 0 8 7. days 4 600 (7.) sec.6 0 6 sec.4.85 0 v 6.6 0 8 05.4/sec v (05.4) a 0.007/sec.7 0 /sec 8.85 0. Diaete of eath 800k
Torque, Angular Momentum and Rotational Kinetic Energy
Toque, Angula Moentu and Rotational Kinetic Enegy In ou peious exaples that inoled a wheel, like fo exaple a pulley we wee always caeful to specify that fo the puposes of the poble it would be teated as
RAYLEIGH'S METHOD Revision D
RAYGH'S METHOD Revisio D B To Irvie Eail: toirvie@aol.co Noveber 5, Itroductio Daic sstes ca be characterized i ters of oe or ore atural frequecies. The atural frequec is the frequec at which the sste
Balancing. Rotating Components Examples of rotating components in a mechanism or a machine. (a)
alacig NOT COMPLETE Rotatig Compoets Examples of rotatig compoets i a mechaism or a machie. Figure 1: Examples of rotatig compoets: camshaft; crakshaft Sigle-Plae (Static) alace Cosider a rotatig shaft
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
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
THE ANALYTIC LARGE SIEVE
THE ANALYTIC LAGE SIEVE 1. The aalytic lage sieve I the last lectue we saw how to apply the aalytic lage sieve to deive a aithmetic fomulatio of the lage sieve, which we applied to the poblem of boudig
MA 1201 Engineering Mathematics MO/2017 Tutorial Sheet No. 2
BIRLA INSTITUTE OF TECHNOLOGY, MESRA, RANCHI DEPARTMENT OF MATHEMATICS MA Egieeig Matheatis MO/7 Tutoia Sheet No. Modue IV:. Defie Beta futio ad Gaa futio.. Pove that,,,. Pove that, d. Pove that. & whee
Physics 4A Chapter 8: Dynamics II Motion in a Plane
Physics 4A Chapte 8: Dynamics II Motion in a Plane Conceptual Questions and Example Poblems fom Chapte 8 Conceptual Question 8.5 The figue below shows two balls of equal mass moving in vetical cicles.
School of Mechanical Engineering Purdue University. ME375 Frequency Response - 1
Case Study ME375 Frequecy Respose - Case Study SUPPORT POWER WIRE DROPPERS Electric trai derives power through a patograph, which cotacts the power wire, which is suspeded from a cateary. Durig high-speed
Lecture 25 (Dec. 6, 2017)
Lecture 5 8.31 Quatum Theory I, Fall 017 106 Lecture 5 (Dec. 6, 017) 5.1 Degeerate Perturbatio Theory Previously, whe discussig perturbatio theory, we restricted ourselves to the case where the uperturbed
I PUC MATHEMATICS CHAPTER - 08 Binomial Theorem. x 1. Expand x + using binomial theorem and hence find the coefficient of
Two Maks Questios I PU MATHEMATIS HAPTER - 08 Biomial Theoem. Epad + usig biomial theoem ad hece fid the coefficiet of y y. Epad usig biomial theoem. Hece fid the costat tem of the epasio.. Simplify +
Rotational Motion: Statics and Dynamics
Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation
1. Hydrogen Atom: 3p State
7633A QUANTUM MECHANICS I - solutio set - autum. Hydroge Atom: 3p State Let us assume that a hydroge atom is i a 3p state. Show that the radial part of its wave fuctio is r u 3(r) = 4 8 6 e r 3 r(6 r).
JEE(MAIN) 2018 TEST PAPER WITH ANSWER (HELD ON SUNDAY 08 th APRIL, 2018) PART C PHYSICS. 64. The density of a material in the shape of a cube ALLEN
6. The agula width of the cetal maximum i a sigle slit diffactio patte is 60. The width of the slit is mm. The slit is illumiated by moochomatic plae waves. If aothe slit of same width is made ea it, Youg
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
Classical 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
Dynamic Response of Linear Systems
Dyamic Respose of Liear Systems Liear System Respose Superpositio Priciple Resposes to Specific Iputs Dyamic Respose of st Order Systems Characteristic Equatio - Free Respose Stable st Order System Respose
Strong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA
Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics
Løsningsførslag i 4M
Norges tekisk aturviteskapelige uiversitet Istitutt for matematiske fag Side 1 av 6 Løsigsførslag i 4M Oppgave 1 a) A sketch of the graph of the give f o the iterval [ 3, 3) is as follows: The Fourier
Construction of mixed estimation for solving the first edge problem for the equation of non-isotropic diffusion
ISSN: 350-038 Iteatioa Joua of AdvacedReseach i Sciece, Egieeig ad echoogy Vo. 5, Issue, Decembe 08 Costuctio of mixed estimatio fo sovig the fist edge pobem fo the equatio of o-isotopic diffusio okhi
Strong Result for Level Crossings of Random Polynomials
IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh
Physics C Rotational Motion Name: ANSWER KEY_ AP Review Packet
Linea and angula analogs Linea Rotation x position x displacement v velocity a T tangential acceleation Vectos in otational motion Use the ight hand ule to detemine diection of the vecto! Don t foget centipetal
KEPLER S LAWS AND PLANETARY ORBITS
KEPE S AWS AND PANETAY OBITS 1. Selected popeties of pola coodinates and ellipses Pola coodinates: I take a some what extended view of pola coodinates in that I allow fo a z diection (cylindical coodinates
Physics 11 Fall 2012 Practice Problems 4 - Solutions
Phsics 11 Fall 01 Pactice Poblems 4 - s 1 Estimate the widest stace ou ca take whe stadi o a d, ic suface That is, how wide ca ou safel place ou feet o ot slip ito a udesied split? Let the coefficiet of
FAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK
The 4 th Wold Cofeece o Eathquake Egieeig Octobe -7, 8, Beijig, Chia FAR FIELD SOLUTION OF SH-WAVE BY CIRCULAR INCLUSION AND LINEAR CRACK HogLiag Li,GuoHui Wu, Associate Pofesso, Depatmet of Egieeig Mechaics,
Ch. 4: FOC 9, 13, 16, 18. Problems 20, 24, 38, 48, 77, 83 & 115;
WEEK-3 Recitation PHYS 3 eb 4, 09 Ch. 4: OC 9, 3,, 8. Pobles 0, 4, 38, 48, 77, 83 & 5; Ch. 4: OC Questions 9, 3,, 8. 9. (e) Newton s law of gavitation gives the answe diectl. ccoding to this law the weight
Phys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j.
7. We denote the two foces F A + F B = ma,sof B = ma F A. (a) In unit vecto notation F A = ( 20.0 N)ˆ i and Theefoe, Phys 201A Homewok 6 Solutions F A and F B. Accoding to Newton s second law, a = [ (
SOLUTIONS TO EXAM 3. Solution: Note that this defines two convergent geometric series with respective radii r 1 = 2/5 < 1 and r 2 = 1/5 < 1.
SOLUTIONS TO EXAM 3 Problem Fid the sum of the followig series 2 + ( ) 5 5 2 5 3 25 2 2 This series diverges Solutio: Note that this defies two coverget geometric series with respective radii r 2/5 < ad
Formula List for College Algebra Sullivan 10 th ed. DO NOT WRITE ON THIS COPY.
Forula List for College Algera Sulliva 10 th ed. DO NOT WRITE ON THIS COPY. Itercepts: Lear how to fid the x ad y itercepts. Syetry: Lear how test for syetry with respect to the x-axis, y-axis ad origi.
Central Force Motion
Cental Foce Motion Cental Foce Poblem Find the motion of two bodies inteacting via a cental foce. Examples: Gavitational foce (Keple poblem): m1m F 1, ( ) =! G ˆ Linea estoing foce: F 1, ( ) =! k ˆ Two
SOLUTIONS TO CONCEPTS CHAPTER 12
SOLUTONS TO CONCEPTS CHPTE. Given, 0c. t t 0, 5 c. T 6 sec. So, w sec T 6 t, t 0, 5 c. So, 5 0 sin (w 0 + ) 0 sin Sin / 6 [y sin wt] Equation of displaceent (0c) sin (ii) t t 4 second 8 0 sin 4 0 sin 6
2D DSP Basics: Systems Stability, 2D Sampling
- Digital Iage Processig ad Copressio D DSP Basics: Systes Stability D Saplig Stability ty Syste is stable if a bouded iput always results i a bouded output BIBO For LSI syste a sufficiet coditio for stability:
The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j
![The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j](/thumbs/82/85448534.jpg "The z-transform. 7.1 Introduction. 7.2 The z-transform Derivation of the z-transform: x[n] = z n LTI system, h[n] z = re j")
The -Trasform 7. Itroductio Geeralie the complex siusoidal represetatio offered by DTFT to a represetatio of complex expoetial sigals. Obtai more geeral characteristics for discrete-time LTI systems. 7.
. Using our polar coordinate conversions, we could write a
504 Chapte 8 Section 8.4.5 Dot Poduct Now that we can add, sutact, and scale vectos, you might e wondeing whethe we can multiply vectos. It tuns out thee ae two diffeent ways to multiply vectos, one which
Physics 235 Final Examination December 4, 2006 Solutions
Physics 35 Fi Emitio Decembe, 6 Soutios.. Fist coside the two u quks. They e idetic spi ½ ptices, so the tot spi c be eithe o. The Pui Picipe equies tht the ove wvefuctio be echge tisymmetic. Sice the
y = f x x 1. If f x = e 2x tan -1 x, then f 1 = e 2 2 e 2 p C e 2 D e 2 p+1 4
. If f = e ta -, the f = e e p e e p e p+ 4 f = e ta -, so f = e ta - + e, so + f = e p + e = e p + e or f = e p + 4. The slope of the lie taget to the curve - + = at the poit, - is - 5 Differetiate -
Born-Oppenheimer Approximation and Nonadiabatic Effects. Hans Lischka University of Vienna
Bo-Oppeheie Appoxiatio ad Noadiabatic Effects Has Lischa Uivesity of Viea Typical situatio. Fac-Codo excitatio fo the iiu of the goud state. Covetioal dyaics possibly M* ad TS 3. Coical itesectio fuel
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
Lecture 13. Rotational motion Moment of inertia
Lectue 13 Rotational motion Moment of inetia EXAM 2 Tuesday Mach 6, 2018 8:15 PM 9:45 PM Today s Topics: Rotational Motion and Angula Displacement Angula Velocity and Acceleation Rotational Kinematics
Appendix: The Laplace Transform
Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio
Advanced Physical Geodesy
Supplemetal Notes Review of g Tems i Moitz s Aalytic Cotiuatio Method. Advaced hysical Geodesy GS887 Chistophe Jekeli Geodetic Sciece The Ohio State Uivesity 5 South Oval Mall Columbus, OH 4 7 The followig
Effect of Material Gradient on Stresses of Thick FGM Spherical Pressure Vessels with Exponentially-Varying Properties
M. Zamai Nejad et al, Joual of Advaced Mateials ad Pocessig, Vol.2, No. 3, 204, 39-46 39 Effect of Mateial Gadiet o Stesses of Thick FGM Spheical Pessue Vessels with Expoetially-Vayig Popeties M. Zamai
Math 21C Brian Osserman Practice Exam 2
Math 1C Bria Osserma Practice Exam 1 (15 pts.) Determie the radius ad iterval of covergece of the power series (x ) +1. First we use the root test to determie for which values of x the series coverges
Mechanical Vibrations
Mechaical Vibratios Cotets Itroductio Free Vibratios o Particles. Siple Haroic Motio Siple Pedulu (Approxiate Solutio) Siple Pedulu (Exact Solutio) Saple Proble 9. Free Vibratios o Rigid Bodies Saple Proble
Ch3. Asymptotic Notation
Ch. Asymptotic Notatio copyright 006 Preview of Chapters Chapter How to aalyze the space ad time complexities of program Chapter Review asymptotic otatios such as O, Ω, Θ, o for simplifyig the aalysis
Test One (Answer Key)
CS395/Ma395 (Sprig 2005) Test Oe Name: Page 1 Test Oe (Aswer Key) CS395/Ma395: Aalysis of Algorithms This is a closed book, closed otes, 70 miute examiatio. It is worth 100 poits. There are twelve (12)
Math 12 Final Exam, May 11, 2011 ANSWER KEY. 2sinh(2x) = lim. 1 x. lim e. x ln. = e. (x+1)(1) x(1) (x+1) 2. (2secθ) 5 2sec2 θ dθ.
Math Fial Exam, May, ANSWER KEY. [5 Poits] Evaluate each of the followig its. Please justify your aswers. Be clear if the it equals a value, + or, or Does Not Exist. coshx) a) L H x x+l x) sihx) x x L
AIEEE 2004 (MATHEMATICS)
AIEEE 004 (MATHEMATICS) Impotat Istuctios: i) The test is of hous duatio. ii) The test cosists of 75 questios. iii) The maimum maks ae 5. iv) Fo each coect aswe you will get maks ad fo a wog aswe you will
Physics 2102 Lecture: 07 TUE 09 FEB
Physics 2102 Jonathan Dowling Physics 2102 Lectue: 07 TUE 09 FEB Electic Potential II PHYS2102 FIRST MIDTERM EXAM 6 7PM THU 11 FEB 2009 Dowling s Sec. 4 in??? YOU MUST BRING YOUR STUDENT ID YOU MUST WRITE
Circular 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
ADDITIONAL INTEGRAL TRANSFORMS
Chapte IX he Itegal asfom Methods IX.7 Additioal Itegal asfoms August 5 7 897 IX.7 ADDIIONAL INEGRAL RANSFORMS 6.7. Solutio of 3-D Heat Equatio i Cylidical Coodiates 6.7. Melli asfom 6.7.3 Legede asfom
The Discrete Fourier Transform
(7) The Discete Fouie Tasfom The Discete Fouie Tasfom hat is Discete Fouie Tasfom (DFT)? (ote: It s ot DTFT discete-time Fouie tasfom) A liea tasfomatio (mati) Samples of the Fouie tasfom (DTFT) of a apeiodic
CRACK DETECTION IN EULER-BERNOULLI BEAMS ON ELASTIC FOUNDATION USING GENETIC ALGORITHM BASED ON DISCRETE ELEMENT TECHNIQUE
Idia J.Sci.Res.() : 48-5, 04 ISSN:50-08(Olie) ISSN : 0976-876 (Pit) CRACK DEECION IN EULER-BERNOULLI BEAMS ON ELASIC FOUNDAION USING GENEIC ALGORIHM BASED ON DISCREE ELEMEN ECHNIQUE MOJABA GHASEMI a, ALIREZA
10. Universal Gravitation
10. Univesal Gavitation Hee it is folks, the end of the echanics section of the couse! This is an appopiate place to complete the study of mechanics, because with his Law of Univesal Gavitation, Newton
EL2520 Control Theory and Practice
oals EL252 Cotol Theoy ad Pactice Lecte 2: The closed-loop system Mikael Johasso School of Electical Egieeig KTH, Stockholm, Sede Afte this lecte, yo shold: Ko that the closed-loop is chaacteied by 6 tasfe
Most text will write ordinary derivatives using either Leibniz notation 2 3. y + 5y= e and y y. xx tt t
Itroductio to Differetial Equatios Defiitios ad Termiolog Differetial Equatio: A equatio cotaiig the derivatives of oe or more depedet variables, with respect to oe or more idepedet variables, is said