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object-oriented programs: impedance & batons 85✝double time ;Plot myPlot = new Plot () ;myPlot. setTitle ("Satellite orbit about planet");myPlot. setXLabel (" x");myPlot. setYLabel (" y");for ( time = 0.; time
86 chapter 4new features without “breaking” the old ones and in which you may be modifyingcode that you did not write.4.8 Trajectory of a Thrown Baton (Problem)We wish to describe the trajectory of a baton that spins as it travels through theair. On the left in Figure 4.6 the baton is shown as as two identical spheres joinedby a massless bar. Each sphere has mass m and radius r, with the centers of thespheres separated by a distance L. The baton is thrown with the initial velocity(Figure 4.6 center) corresponding to a rotation about the center of the lowersphere.Problem: Write an OOP program that computes the position and velocity of thebaton as a function of time. The program should1. plot the position of each end of the baton as a function of time;2. plot the translational kinetic energy, the rotational kinetic energy, and thepotential energy of the baton, all as functions of time;3. use several classes as building blocks so that you may change one buildingblock without affecting the rest of the program;4. (optional) then be extended to solve for the motion of a baton with anadditional lead weight at its center.4.8.1 Combined Translation and Rotation (Theory)Classical dynamics describes the motion of the baton as the motion of its centerof mass (CM) (marked with an “X” in Figure 4.6), plus a rotation about the CM.Because the translational and rotational motions are independent, each may bedetermined separately, and because we ignore air resistance, the angular velocityω about the CM is constant.The baton is thrown with an initial velocity (Figure 4.6 center). The simplest wayto view this is as a translation of the entire baton with a velocity V 0 and a rotationof angular velocity ω about the CM (Figure 4.6 right). To determine ω, we note thatthe tangential velocity due to rotation isv t = 1 ωL. (4.20)2For the direction of rotation as indicated in Figure 4.6, this tangential velocity isadded to the CM velocity at the top of the baton and is subtracted from the CMvelocity at the bottom. Because the total velocity equals 0 at the bottom and 2V 0 atthe top, we are able to solve for ω:12 ωL − V 0 =0 ⇒ V 0 = 1 2 ωL, ⇒ ω = 2V 0L . (4.21)−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 86
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COPYRIGHT 2008, PRINCET O N UNIVE R
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−101COPYRIGHT 2008, PRINCET O N U
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Copyright © 2008 by Princeton Univ
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viiicontents2.3 Experimental Error
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xcontents6.3 Experimentation 1356.4
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xiicontents9.7.1 Friction: Model an
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xvicontents14.15.2Exercise 2: Cache
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xxcontentsC.3 DX Tools Summary 576C
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xxivprefacewhich includes understan
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2 chapter 1PhysicsCPFigure 1.1 A re
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4 chapter 1Scientific LibrariesPerf
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6 chapter 1C DWe have tried to make
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8 chapter 1possibly when installing
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10 chapter 11.4.1 Structured Progra
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12 chapter 17. Revise Area.java so
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14 chapter 1argv). Because main met
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16 chapter 1Package Class Tree Depr
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18 chapter 1Memory and storage size
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20 chapter 1TABLE 1.4The IEEE 754 S
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22 chapter 1gives 24-bit precision
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24 chapter 1TABLE 1.6Representation
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26 chapter 1The computer fetches th
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28 chapter 1Your problem is to use
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2Errors & Uncertainties in Computat
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32 chapter 2purposes, let us consid
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136 chapter 6the integral of f(x)=1
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138 chapter 6f(x)< f(x) >xFigure 6.
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140 chapter 61. Conduct 16 trials a
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142 chapter 6acceptrejectFigure 6.6
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144 chapter 6The crux of this techn
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7Differentiation & SearchingIn this
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148 chapter 7the forward-difference
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150 chapter 7algorithm (7.7) is O(h
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152 chapter 7algorithms in which de
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154 chapter 7we know a zero occurs.
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156 chapter 7Figure 7.3 Two example
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8Solving Systems of Equationswith M
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160 chapter 8the spheres, and the d
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162 chapter 8We now have a solvable
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164 chapter 8of (8.19) by A −1 :x
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166 chapter 8Row MajorColumn Majora
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168 chapter 8having different varia
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170 chapter 8Matrix objects, add an
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172 chapter 8✞/∗ JamaFit : JAMA
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174 chapter 8( ) α β3. Consider t
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176 chapter 8discarding some inform
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178 chapter 8Lagrange interpolation
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180 chapter 8Figure 8.3 Three fits
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182 chapter 8if you have the abilit
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184 chapter 840fitNumber20dataN(t)0
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186 chapter 8theoretical curve went
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188 chapter 8This is a measure of t
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190 chapter 88.7.4 Linear Quadratic
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192 chapter 8Your problem here is t
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9Differential Equation Applications
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196 chapter 9V(x)HarmonicAnharmonic
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198 chapter 9B(t) are solutions of
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200 chapter 9This expresses the acc
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202 chapter 9derivative:dy(t)dt≃
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204 chapter 9As an example of the u
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206 chapter 9C Dhigh-precision work
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208 chapter 9Amplitude Dependence,
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210 chapter 9Here N is the normal f
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212 chapter 99.9 Unit II. Binding A
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216 chapter 99.11.1 Numerov Algorit
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222 chapter 99.13 Unit III. Scatter
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224 chapter 9The equations for the
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226 chapter 9Figure 9.9 The traject
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230 chapter 99.17.1.1 EXPLORATION:
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232 chapter 10y(t)10Y( )10-1t-10 20
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234 chapter 10As seen in the b n co
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236 chapter 1010.4 Fourier Transfor
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238 chapter 10Regardless of the act
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240 chapter 10for the exponential a
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242 chapter 10102 4 6-1Figure 10.2
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244 chapter 10coefficients a k . If
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246 chapter 104. As always, check t
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248 chapter 10A special case of the
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256 chapter 1010.8 Unit III. Fast F
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258 chapter 10Figure 10.9 The basic
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260 chapter 10TABLE 10.1Binary-Reve
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262 chapter 10✞/∗ FFT. java : F
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11Wavelet Analysis & Data Compressi
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266 chapter 11the second derivative
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268 chapter 1111.2.1 Wave Packet As
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270 chapter 11localized in time, su
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272 chapter 11201 Y100Signal0-10-10
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274 chapter 11you have been using f
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278 chapter 11FrequencyTimeFigure 1
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280 chapter 11N SamplesInputN/2(1)c
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wavelet analysis & data compression
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288 chapter 113. Reproduce the scal
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290 chapter 12discrete decay law,
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292 chapter 120.80.400 10 20Ax nn n
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302 chapter 1212.10 Unit II. Pendul
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306 chapter 12Figure 12.6 The data
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308 chapter 12rotating solutionsθ2
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Angular Velocity of Lower Pendulum3
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324 chapter 12400200pPopulationpP00
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13Fractals & Statistical GrowthIt i
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328 chapter 1330010,000 points20010
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332 chapter 13copy of a frond, and
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334 chapter 13The results of this t
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336 chapter 13log N(r) = log C −
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338 chapter 13to determine the slop
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340 chapter 13✞☎import java . i
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342 chapter 13Figure 13.8 Number 8
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344 chapter 13Conway in the 1970s,
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346 chapter 13(x 0, y 1)(x 0, y 0)(
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348 chapter 13yxFigure 13.13 After
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350 chapter 13gradient // Vertical
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14High-Performance Computing Hardwa
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354 chapter 14A(1)A(2)A(3)CPUA(N)M(
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356 chapter 14ADBCFigure 14.4 Multi
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358 chapter 14as Fortran or C, tran
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360 chapter 14TABLE 14.2Computation
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362 chapter 14The processors in a p
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364 chapter 14Figure 14.7 Two views
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366 chapter 14Speedup8Amdahl's Lawp
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368 chapter 1414.11 Parallelization
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370 chapter 14The problem affects p
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372 chapter 14• A race condition
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374 chapter 14yet in order to obtai
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376 chapter 14slightly faster or sm
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378 chapter 14You see (Listing 14.1
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380 chapter 14/optimize:4/optimize:
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382 chapter 14• As indicated in
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384 chapter 1410,000Execution Time
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386 chapter 14as high-performance c
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388 chapter 14✞Dimension Vec( idi
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16Simulating Matter withMolecular D
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426 chapter 16+ +Figure 16.1 The mo
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428 chapter 16the molecules stay cl
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430 chapter 162 3 2 3 2 31 4 1 4 1
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432 chapter 16Velocity-Verlet Algor
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434 chapter 16Energy vs Timefor 36
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thermodynamic simulations & feynman
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17PDEs for Electrostatics & Heat Fl
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θpde waves: string, quantum packet
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pde waves: string, quantum packet,
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solitons & computational fluid dyna
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✞solitons & computational fluid d
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integral equations in quantum mecha
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✞integral equations in quantum me
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Appendix A: Glossaryabsolute value
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glossary 557control character — A
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glossary 559log in (on) — To sign
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glossary 561supercomputer — The c
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installing ptplot & java developer
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industrial-strength data visualizat
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Appendix D: An MPI TutorialIn this
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an mpi tutorial 595• Open a shell
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an mpi tutorial 597of all the compu
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an mpi tutorial 599TABLE D.1Some Co
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an mpi tutorial 601jobs to MPI. 2 A
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an mpi tutorial 603✞> cd $HOME Do
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an mpi tutorial 605✞/ / MPIhello
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an mpi tutorial 607Argument Namemsg
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an mpi tutorial 609D.3.4 Broadcast
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an mpi tutorial 611D.4 Parallel Tun
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an mpi tutorial 613✝}MPI_Recv ( &
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an mpi tutorial 615✞/ / Code list
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an mpi tutorial 617-1) does not sen
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an mpi tutorial 619D.6.1 Nonblockin
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an mpi tutorial 621D.9 List of MPI
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Appendix E: Calling LAPACK from CCa
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calling LAPACK from C 625E.2 Compil
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software on the CD 627JavaCodes Con
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software on the CD 629JavaCodes Con
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software on the CD 631Applets Direc
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software on the CD 633Fortran77code
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Appendix G: Compression via DWTwith
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compression via DWT with thresholdi
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compression via DWT with thresholdi
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BIBLIOGRAPHY[Abar 93] Abarbanel, H.
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ibliography 643[Erco] Ercolessi, F.
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ibliography 645[L&F 93] Landau, R.
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ibliography 647[P&W 91] Pinson, L.
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ibliography 649[VdeV 94] van de Vel
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IndexAbstract data structures,70Abs
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index 653drand, 114Driving force, 2
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index 655Libraries, see Subroutines
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index 657structured, 10for virtual
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