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不错的汽车动力学教材，是参与汽车底盘电子开发的动力学基础。Reza n. jazarVehicle DynamicsTheory and ApplicationsSpringerReza n. jazarDept of Mechanical EngineeringManhattan collegeRiverdale. NY 10471ISBN:978-0-387-74243-4e-ISBN:978-0-387-74244-1Library of Congress Control Number: 200794219c 2008 Springer Science+ Business Media, LLCAll rights reserved. This work may not be translated or copied in whole or in part without thewritten permission of the publisher(Springer Science+Business Media, LLC, 233 SpringStreet, New York, NY 10013, USA), except for brief excerpts in connection with reviews orscholarly analysis. Use in connection with any form of information storage and retrievalelectronic adaptation, computer software, or by similar or dissimilar methodology now knownor hereafter developed is forbidden. The use in this publication of trade names, trademarksservice marks and similar terms, even if they are not identified as such, is not to be taken as anexpression of opinion as to whether or not they are subject to proprietary rightsPrinted on acid-free paper987654321springer. comKavoshmy daughter, Vazan,and my wife, MojganHappiness is when you win a race against yourselfPrefaceThis text is for engineering students. It introduces the fundamental knowledge used in vehicle dymamics. This knowledge can be utilized to developcomputer programs for analyzing the ride, handling, and optimization ofroad vehiclesVehicle dynamics has been in the engineering curriculum for more thana hundred years. Books on the subject are available, but most of themare written for specialists and are not suitable for a classroom applicationA new student, engineer, or researcher would not know where and howto start learning vehicle dynamics. So, there is a need for a textbook forbeginners. This textbook presents the fundamentals with a perspective onfuture trendsThe study of classical vehicle dynamics has its roots in the work ofgreat scientists of the past four centuries and creative engineers in thepast century who established the methodology of dynamic systems. Thedevelopment of vehicle dynamics has moved toward modeling, analysisand optimization of multi-body dynamics supported by some compliantmembers. Therefore, merging dynamics with optimization theory was anexpected development. The fast-growing capability of accurate positioninsensing, and calculations, along with intelligent computer programming arethe other important developments in vehicle dynamics. So, a textbook helpthe reader to make a computer model of vehicles, which this book doesLevel of the bookThis book has evolved from nearly a decade of research in nonlineardynamic systems and teaching courses in vehicle dynamics. It is addressedprimarily to the last year of undergraduate study and the first year graduatestudent in engineering. Hence, it is an intermediate textbook. It providesboth fundamental and advanced topics. The whole book can be coveredin two successive courses, however, it is possible to jump over some sections and cover the book in one course. Students are required to know thefundamentals of kinematics and dynamics, as well as a basic knowledge ofnumerical methodsThe contents of the book have been kept at a fairly theoretical-practicallevel. Many concepts are deeply explained and their application empha-sized, and most of the related theories and formal proofs have been explained. The book places a strong emphasis on the physical meaning andapplications of the concepts. Topics that have been selected are of highinterest in the field. An attempt has been made to expose students to aPrefacebroad range of topics and approachese There are four special chapters that are indirectly related to vehicle dy-amics: Applied Kinematics, Applied Mechanisms, Applied dynamics, andApplied vibrations. These chapters provide the related background to understand vehicle dynamics and its subsystemsOrganization of the bookThe text is organized so it can be used for teaching or for self-studyChapter 1"Fundamentals, "contains general preliminaries about tire andrim with a brief review of road vehicle classificationsPart I"One Dimensional Vehicle Dynamics, " presents forward vehicledynamics, tire dynamics, and driveline dynamics. Forward dynamics refersto weight transfer, accelerating braking, engine performance, and gear ratiodesignPart II"Vehicle Kinematics, presents a detailed discussion of vehiclemechanical subsystems such as steering and suspensionsPart IIT"Vehicle Dynamics, employs Newton and Lagrange methodsto develop the maneuvering dynamics of vehiclesPart Iv "Vehicle Vibrations, presents a detailed discussion of vehi-cle vibrations. An attempt is made to review the basic approaches anddemonstrate how a vehicle can be modeled as a vibrating multiple degreeof-freedom system. The concepts of the Newton-Euler dynamics and La-grangian method are used equally for derivation of equations of motionThe RMS optimization technique for suspension design of vehicles is intro-duced and applied to vehicle suspensions. The outcome of the optimizationtechnique is the optimal stiffness and damping for a car or suspended equipmentMethod of presentationThis book uses a fact-reason-application"structure. The "fact"is themain subject we introduce in each section. Then the reason is given as a" proof. The application of the fact is examined in some examples. Theexamplesare a very important part of the book because they show howto implement the facts. They also cover some other facts that are neededto expand the subjectPrerequisitesSince the book is written for senior undergraduate and first-year graduatelevel students of engineering, the assumption is that users are familiar withmatrix algebra as well as basic dynamics. Prerequisites are the fundamentals of kinematics, dynamics, vector analysis, and matrix theory. Thesebasics are usually taught in the first three undergraduate yearsPrefaceUnit SystemThe system of units adopted in this book is, unless otherwise stated, theinternational system of units(SI). The units of degree(deg)or radian(rad)are utilized for variables representing angular quantitiesSymbolse Lowercase bold letters indicate a vector. Vectors may be expressed inan n dimensional Euclidian space. ExamplerCUppercase bold letters indicate a dynamic vector or a dynamic matrix, such as force and moment. ExampleFo Lowercase letters with a hat indicate a unit vector. Unit vectors arenot bolded. ExampleLowercase letters with a tilde indicate a 3 x 3 skew symmetric matrixassociated to a vector. Examplea3211An arrow above two uppercase letters indicates the start and endpoints of a position vector. ExampleON = a position vector from point o to point Ne The length of a vector is indicated by a non-bold lowercase letterExampleCapital letter B is utilized to denote a body coordinate frame. ExampleB(ocgB(Oxyz)B1(o1x19121)ⅹ11PrefaceCapital letter G is utilized to denote a global, inertial, or fixed coordinate frame. ExampleG(XYZG(OXYZRight subscript on a transformation matrix indicates the departureframes. ExampleRB= transformation matrix from frame B(oxyz)Left superscript on a transformation matrix indicates the destinationframe. ExampleRBtransformation matrix from frame B(o cgz)to frame G(OxYZ)Capital letter R indicates rotation or a transformation matrix, if itshows the beginning and destination coordinate frames. Example0BSIn a0Whenever there is no sub or superscript, the matrices are shown in abracket. ExampleCOS asin a osIn aCOs O0e Left superscript on a vector denotes the frame in which the vectoris expressed. That superscript indicates the frame that the vectorbelongs to; so the vector is expressed using the unit vectors of thatEr= position vector expressed in frame G(OXYZ)Right subscript on a vector denotes the tip point that the vector isreferred to. ExamplePsition vector ofexpressed in coordinate frame G(OXYZ)Right subscript on an angular velocity vector indicates the frame thatthe angular vector is referred to. ExampleB= angularof the body coordinate frame B(oxyz)

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用于验证回声消除算法效果的音频测试文件，长度从十几秒到几分钟不等，左声道是近端信号、右声道是远端信号。

计算理论复习总结,但是考试快要结束了，估计大家也没有什么需要了。28.文法是CFG的推广,任何CFG都是文法。G=(V,∑,R,S)29.语言被文法生成ⅲ它是re的。30.所有数值函数都是原始递归的31.原始递归函数集是递归可枚举的。32.特殊语言/问题H={"M"w":M在w上停机}lH={"M"w":M是一台在"w"上不停机的TM}H1={"M":M在“M”上停机}H1={w:要么w不是一台TM的编码,要么w是M的编码,M是一台在"M"上不停机的TM}H:re.;H1:re.;-H,-H1:非r.e.;2-SAT∈P;SAT∈NPThe world as We Dont Know itreAsumming P≠APCo『eHrecursiveSATSATCO-A伊II Asumming P=Npr, eCo-r.erecursiveNP= cO-Np= p33没有算法的问题称作不可判定的or不可解的,如TM的停机问题34.证明不可判定通用图灵机U通过递归函数归约到L如果L是递归的则U是递归的ic若L1非递归,并存在L1到L2的归约,则L2也非递归。递归函数是 Turing Computable的35.语言是图灵可枚举的,证存在枚举它的图灵机。(M通过空格代开始,周期性的经过特殊状态q来枚举L,任意顺序且可重复)6.不可判定语言与递归语言互为补集,与rc语言有交集。37语言是re.,if它是图灵可枚举的;语言是递归的,i它是以字典序 turing可枚举的。8.P在并交连接和补运算下封闭NP在并、连接运算下封闭。若NP在补下封闭则NP=P39.H={M"wM在最多2w步后停机}唾P40.所有正则语言和所有CFL都属于P41.NPA.机器角度去定义:被多项式界限非确定型图灵机判定的所有语言的类。B.基于 verifier的定义:NP问题上建立的非确定机包含两步1)非确定地猜一个解2〕用一个确定的算法判定该解是否为可行解判定一个给定猜测值是否满足该问题(可满足性)的算法称作 verifier,一个问题称作NP问题当且仅当存在一个多项式时间的 verifier这两个定义是不矛盾的,因为如果一台非确定TM在多项式时间内可以判定一个非确定选择的翰入是否满足,就是基于 verifier的定义。P和NP的区别a problem is in P if we can decide them in polynomial time. It is in NP if we candecide them in polynomial time, if we are given the right certificate42.若存在计算函数f的多项式界限的图灵机M,则f称为多项式时间可计算的43.若τ1是L1->l2的多项式归约,τ2是L2->I3的多项式归约,则τ1τ2是L1->l3的多项式归约44.证明NP完全法一、按定义:LΣ*,若(a)L∈NP,且(b)对每个语言L∈NP,存在从L到L的多项式归约则L称为NP完全的。法二、归约,对于语言L,(a)若L∈NP(b)一个NP完全问题可以在多项式时间规约到L,ie. SAT 0 is context-free but not regular49.L=L1L2,L是CFL,则L1一定是CFL(x50. Regular-CFL不一定是CFL,如a*b*c*-anbn包含 anben51. 2-way PDalie PDa whose input heads can move both left and right] are more powerfulthan 1-way pda52. Given a PDa M1 and an fa M2, the problem l(M1)cl(M2)is decidable53.DFA/NFA识别的是 exactly正则语言54.Re.只在补和差下不封闭,CFL在交下也不封闭55.非正则语言的可能是正则语言。比如A:[W=w}及所有回文,A=*,为正则语言56.典型非正则:w=wR57.正则语言的子集可能非正则,如 anben是a*b*c*的子集;又如Σ*是正则语言,H≌Σ*58.归约:X到Y的归约可以理解为X到Y问题的映射, reduction可以解释为 at least asdifficult as….比如ⅹ可以被Y的算法解决,则 X is no more difficult than yⅩ可以约到Y,记X≤Y。e.gx2可以归约到任意两数的乘积。若有A≤B,A是不可判定问题>B不可判定A不递归->B不递归B可判定>A可判定B是递归的->A是递归的59.若X多项式时间归约到Y,Y多项式时间可解,则X多项式时间可解若X多项式时间归约到Y,Ⅹ多项式时间不可解,则Y多项式时间不可解60.X多项式时间归约到Y,Y多项式时间归约到Z,则X多项式时间归约到Z61.PRME( COMPOSITE)多项式时间归约到 Factor,但是 Factor多项式时间不能归约到PRIME COMPOSITE )o62.若A≤PB,B∈NP,则A∈NP。证明A≤PB→存在确定图灵机X,可将A归约到B。B∈NP→存在一个非确定图灵机N可判定B。我们希望构造一个新的TM(ⅹN)是的ⅹ*N非确定多项式时间求解A,则A∈NPRunning time of X*N≤1+p(mB>+qp(m)(B多项式时间非确定判定是多项式时间所以A∈NP63若AsPB,B∈P,则A∈P64.若X是NPC的,则X在多项式时间内可解ifP=NP65.SAT多项式时间归约到3SA(3AT是NPC的)66.证明语言L是R/Re, Non rea) Intuitively想想有没有半判定(判定)的TM,有则Rc、(R)。若非R执行下一步。b)用能否由Re.( Non re.)语言归约到该语言,能则Re而非R( Non re)严格用归约函数定义f:A≤B,r1∈A当且仅当r1∈Beg1∈H,M∈L证明Recg2∈非H,iM∈L证明 Non rc注意方向:是从A的实例经过递归函数推向B的实例。详细介绍http://www.cs.rice.edu/nakhleh/comp481/finalreviewsp06sol.pdf67.递归与μ递归等价68.PDA中,若每一个格局至多有一个格局接在它后面,则为确定型的。确定型CF在补下封闭69.M半判定L:w∈L,ifM在w上停机,注意半判定图灵机中不存在“拒绝”状态。只要不接受w,就不停机。70. Chomsky hierarchyElements of the Chomsky HierarchyRecursively enumerable languagesRecursive languageContext sensitive languagesContext ee languageseterministccontext free languagesRegularanguages71.俩证明7.6证明P在并、交、 Kleene*连接和补运算下封闭(1)并:对任意L,LEP,遴n时间图灵机M1和nb时间图灵机M2判定它们且c=max{ab}对L1L2构造判定器MM=“对于输入字符串w1)在W上运行M1,在w上运行M22)若有一个接受则接受,否则拒绝。时间复杂度:设M1为0(n)M2为0(m)。令c=max{ab}第一步用时0(n+n),因此总时间为Oma+n)=0(n9所以L1L2属于P类,即P在并的运算下封闭。(2)连接对任意L1,L2属于P类,设有n时间图灵机M1和m时间图灵机M2判定它们,且c=max{ab}。对L1l2构造判定器MM=“对于输入字符串w=w2灬,Wn对k=0,1,21…,n重复下列步骤。在wW2…wk上运行M1,在wk1wk+2…n上运行M若都接受,则接受。否则继续。若对所有分法都不接受则拒绝。时间复杂度:(n+1x0(n+0m-0(m+4)+0(nb+4=0(nc+),F以L1oL2属于P类,即P在连接的运算下封闭。对任意L属于P类,设有时间0(n)判定器M判定它,对构造判定器MM=“对于输入字符串〔1)在w上运行M12)若M1接受则拒绝,若M1拒绝则接受。时间复杂度为:0(m)。所以属于P类,即P在补的运算下封闭。77证明NP在并和连接运算下封闭。1)并对任意L1,L2∈NP,设分别有n时间非确定图灵机M1和n时间非确定图灵机M2判定它们,且c=max{a,b}。构造判定LL2的非确定图灵机M:M=“对于输入字符串w1)在W上运行M1,在w上运行M2。2)若有一个接受则接受,否则拒绝。对于每一个非确定计算分支,第一步用时为O(n-)+O(n),因此总时间为On+n)=0(n。所以LLz∈NP,即NP在并的运算下封闭2)连接对任意L,L2∈NP设分别有na时间非确定图灵机M1和m时间非确定图灵机M2判定它们,且c=max{ab}。构造判定L1oL2的非确定图灵机M:M=“对于输入字符串w:1〕非确定地将分成两段xy,使得w=xy。2)在x上运行M1,在y上运行M23)若都接受则接受,否则拒绝。对于每一个非确定计算分支,第一步用时O(n,第二步用时为0(n)+0(m),因此总时间为o(n+m)=0(n。所以L1oL2∈NP,即NP在连接运算下封闭。专题一一图灵机可判定性问题判定以下问题是否可判定:声明:思路—想证明B问题不可解,1.从一个不可解问题A入手(如停机问题)2.创建B的—个实例,从中推出如果能解决B,A也就可以解决了3.所以B是不可解的1.一个图灵机有至少481个状态。我们可以给出这样一个TMN进行cnc(M)a)数M中状态数,直到481b)如果达到了481,N就接受,否则拒绝2.给定图灵机在空串上走了481步还没停机。构造2带图灵机N,a)2a带:写481个0b)1s带在空串上模拟M,每走一步,第2带就删掉一个0c)如果M在所有0都删掉之后停机,则N接受,否则不接受给定图灵机,判定它是否在一些输入上经过481步还没停机?a)按字典序找出所有 length

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