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Műszaki mechanika – kinematika

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dc.contributor.editor Bitay, Enikő
dc.coverage.temporal 2010 hu_HU
dc.creator Máté, Márton
dc.date.accessioned 2011-09-16T10:43:10Z
dc.date.available 2011-09-16T10:43:10Z
dc.date.issued 2010
dc.identifier.isbn 978-606-8178-10-3
dc.identifier.issn 2068 – 3081
dc.identifier.uri http://hdl.handle.net/10598/15439
dc.description.abstract A gyakorlati tudományok jelenkori művelőire hárul az a feladat, hogy a modern eljárások segítségével találják meg a klasszikus, örökérvényű ismeretek megközelítésének azt a módját, mellyel a tudományos fejlődés hatékonyabb mozgatórugóját hozzák létre. A Műszaki mechanika-Kinematika könyv elsősorban a mecha­tronika- és gyártástechnológia- szakos hallgatókhoz szól, de hasznos lehet bárki számára, akinek érdeke az alapvető kinema­tikai ismeretek elsajátítása. Az anyagi pont és az anyagi merev test mozgásának azokat a lényeges sajátosságait tárgyalja, amelyek ismeretében a hallgató bizalommal láthat neki a me­chanikára épülő szaktantárgyak elsajátításához, mint a gépszer­kezettan, gépelemek valamint a robotika. hu_HU
dc.description.abstract This book is firstly recommended for students of faculties of engineering, especially for those studying Mechatronics and Mechanical Engineering. Students interested in acquiring knowledge about kinematics of the rigid body, with application in engineering may also benefit from this material. The basic problems of kinematics presented in three chapters within the book offer the reader fundamental knowledge necessary to comprehend special engineering matter in the semesters to follow. First chapter, “Kinematics of the material point” presents the calculus of motion parameters of the point. Several geometrical applications are added to this content with reference to the calculus of the curvature of the trajectory. Poisson’s formula regarding the derivative of a unit vector versus time is demonstrated for the particular case of plane motion. Chapter II, „Kinematics of the rigid body”, enumerates the most frequent motions with immediate application in the theory of mechanisms as follows: the translation, the rotation over a fixed axis, the helical motion, the plane motion, and the spherical motion. This chapter ends with the analysis of the general motion of the rigid body. The analysis of the motions mentioned before focuses on the study of trajectories, the repartition of velocities and accelerations. Calculus is performed using both vector and matrix methods. The study finally demonstrates in each case the equivalence of matrix and vector formulas. The book presents and compares the two methods, emphasizing the advantages of vector calculus with its simplicity in theoretical models versus the efficiency of the matrix method revealed in practical determinations and modeling. The matrix method has incontestable advantages in computational solutions. Chapter III, “The relative motion” focuses on a detailed analysis of the relative motion in both cases of the material point and the rigid body. The mathematical models were build-up accepting the non-relativistic approach and the validity of the Euclidian space – still an efficient and agreeable approximation for the day to day material existence. Finally I believe that this book will be useful in developing fundamental skills for the kinematic modeling of mechanical structures and will increase the interest of the reader for the matrix calculus, indispensable for building-up modern mathematical models. en
dc.description.abstract Prezenta carte se adresează în primul rând studenţilor facultăţilor de inginerie, în special celor care urmează programele de studiu „Mecatronică” respectiv „Tehnologia construcţiilor de maşini”, dar poate fi utilă tuturor celor care doresc să dobândească cunoştinţe fundamentale despre cinematica rigidului, cu aplicaţii în tehnică. Lucrarea tratează, în trei capitole, problemele de bază ale cinematicii, cu propunerea pregătirii unui fundament solid de cunoştinţe, în vederea accesării disciplinelor tehnice de domeniu şi de specialitate, din anii superiori, care se bazează pe mecanică. Primul capitol, intitulat „Cinematica punctului material”, prezintă modalitatea de calcul al parametrilor cinematici ai punctului, adăugând, unde este cazul, şi aplicaţii geometrice, privind calculul curburii curbei traiectorie, într-un punct dat, dacă se cunoaşte legea de mişcare. Se demontrează formula lui Poisson cu privire la derivata vectorului unitar în funcţie de timp, pentru cazul particular al mişcării în plan. Capitolul II, „Cinematica solidului rigid”, trece în revistă cele mai întâlnite tipuri de mişcări particulare ale corpului solid, cu aplicaţie imediată în teoria mecanismelor: mişcarea de translaţie, mişcarea de rotaţie cu axă fixă, mişcarea elicoidală, mişcarea plan-paralelă şi mişcarea de rotaţie cu punct fix. Prezentarea se încheie prin analiza mişcării generale a rigidului. Problemele care se pun la analiza acestor mişcări vizează analiza traiectoriilor, distribuţia vitezelor şi cea a acceleraţiilor. Analiza este efectuată atât pe cale vectorială, cât şi matriceal, calculul terminându-se de fiecare dată prin demonstraţia identităţii relaţiilor vectoriale cu cele matriceale. S-a urmărit utilizarea simultană a celor două metode pentru a pune în evidenţă avantajele relaţiilor vectoriale în calculele teoretice, şi a celor matriceale, în determinările practice. Se accentuează posibilităţile vaste care sunt cuprinse în modul matriceal de conducere ale calculelor, mai ales posibilitatea automatizării acestora. Capitolul III, „Mişcarea relativă”, încheie cartea, prin prezentarea detaliată a mişcării punctului, cât şi al rigidului. Relaţiile de calcul şi modelele matematice prezentate sunt deduse în ipoteză nerelativistă, cu acceptarea proprietăţilor geometrice ale spaţiului euclidian – încă o eficientă şi plăcută aproximaţie a existenţei materiale cotidiene. Îmi exprim speranţa că, în urma parcurgerii celor trei capitole, cititorul va dobândi siguranţa necesară modelării cinematice ale structurilor mecanice, şi i se va stârni interesul pentru calculul matriceal – indispensabil în abordarea modernă a modelelor matematice. ro_RO
dc.description.tableofcontents Előszó ............................................................................................................. 9 I. FEJEZET. ANYAGI PONT KINEMATIKÁJA 1.1.Alapfogalmak............................................................................................. 11 1.2. Anyagi pont mozgásparaméterei.............................................................. 12 1.2.1. Anyagi pont pályagörbéje .............................................................. 12 1.2.2. Anyagi pont sebessége.................................................................. 12 1.2.3. Anyagi pont gyorsulása.................................................................. 14 1.2.4. A gyorsulásvektor normál, illetve tangenciális összetevőinek számítása 16 1.2.5. Geometriai alkalmazás .................................................................. 17 1.3. Anyagi pont kinematikája polárkoordonátákban....................................... 18 1.3.1. A mozgás polárkoordonátákra értelmezett sajátosságai............... 18 1.3.2. Anyagi pont sebessége polárkoordonátás felírásban.................... 20 1.3.3. Anyagi pont gyorsulása polárkoordonátás felírásban.................... 20 1.3.4. A szögsebesség vektorizálása....................................................... 22 II. FEJEZET. ANYAGI TESTEK KINEMATIKÁJA 2.1.Alapfogalmak............................................................................................. 23 2.2. Egyszerű mozgások ................................................................................. 24 2.2.1. A haladó mozgás ........................................................................... 24 A. Vektormódszer ............................................................................... 24 B. Mátrixmódszer ................................................................................ 26 2.2.2. Az állandó tengelyes forgómozgás................................................ 28 A. Vektormódszer ............................................................................... 28 2.2.2.1. A sebességeloszlás.................................................................. 29 2.2.2.2. A gyorsuláseloszlás.................................................................. 31 B. Mátrixmódszer ................................................................................ 34 2.2.2.3. A mozgástörvény mátrixos értelmezése .................................. 34 2.2.2.4. A sebesség mátrixos alakja...................................................... 36 2.2.2.5. A gyorsulás mátrixos alakja...................................................... 37 2.3. Összetett mozgások ................................................................................. 39 2.3.1. A csavarmozgás............................................................................. 39 A. Vektormódszer ............................................................................... 40 2.3.1.1. A sebességeloszlás.................................................................. 41 2.3.1.2. A gyorsuláseloszlás.................................................................. 43 B. Mátrixmódszer ................................................................................ 46 2.3.1.3. A csavarmozgás mátrixmodellje............................................... 46 2.3.1.4. A sebesség mátrixos alakja...................................................... 47 2.3.1.5. A gyorsulás mátrixos alakja...................................................... 49 2.3.2. A síkmozgás................................................................................... 51 A. Vektormódszer ............................................................................... 53 2.3.2.1. A sebességeloszlás.................................................................. 53 2.3.2.2. A sebességpólus ...................................................................... 57 2.3.2.3. A centroida-görbék ................................................................... 58 2.3.2.4. Gyakorlati műszaki alkalmazások ............................................ 60 2.3.2.5. Grafikus módszerek ................................................................. 61 2.3.2.6. A gyorsuláseloszlás.................................................................. 63 2.3.2.7. A gyorsuláspólus ...................................................................... 64 2.3.2.8. A gyorsulás tulajdonságai ........................................................ 65 2.3.2.9. A gyorsulás geometriai értelmezése ........................................ 67 B. Mátrixmódszer ................................................................................ 69 2.3.2.10. A sebességeloszlás mátrixos tárgyalása ............................... 69 2.3.2.11. A centroidák mátrixos alakja .................................................. 71 2.3.2.12. A centroidák kölcsönös burkolása.......................................... 73 2.3.2.13. A gyorsuláseloszlás mátrixos számítása ............................... 75 2.3.2.14. A gyorsuláspólus .................................................................... 76 2.3.3. A gömbmozgás .............................................................................. 77 2.3.3.1. A gömbmozgás meghatározása............................................... 77 2.3.3.2. A gömbmozgás szabadsága.................................................... 79 2.3.3.3. A gömbmozgás pályaegyenletei .............................................. 80 A. Általános megfogalmazás .............................................................. 80 B. A pályagörbe tárgyalása Euler-szögekkel...................................... 81 C. A pályagörbe tárgyalása elemi forgatásokkal ................................ 83 2.3.3.4. A sebességeloszlás.................................................................. 84 A. Vektormódszer ............................................................................... 84 B. Mátrixmódszer ................................................................................ 87 2.3.3.5. Axoidfelületek ........................................................................... 91 2.3.3.6. A gyorsuláseloszlás.................................................................. 93 A.Vektormódszer ................................................................................ 93 B. Mátrixmódszer ................................................................................ 97 2.3.3.7. A gyorsuláspólus tanulmányozása......................................... 100 2.3.4. Az általános mozgás.................................................................... 102 2.3.4.1. A mozgás értelmezése........................................................... 102 2.3.4.2. Adott pont pályagörbéjének egyenletei .................................. 105 A. Vektormódszer ............................................................................. 105 B. Mátrixmódszer .............................................................................. 107 2.3.4.3. A sebességeloszlás................................................................ 109 A. Vektormódszer ............................................................................. 109 B. Mátrixmódszer .............................................................................. 112 2.3.4.4. A pillanatnyi forgástengely létezésének feltétele ................... 115 2.3.4.5. A pillanatnyi csavartengely..................................................... 120 2.3.4.6. A gyorsuláseloszlás................................................................ 126 A. Vektormódszer ............................................................................. 126 B. Mátrixmódszer .............................................................................. 127 2.3.4.7. A gyorsuláspólus .................................................................... 129 III. FEJEZET. A RELATÍV MOZGÁS 3.1. A relatív mozgás értelmezése ................................................................ 133 3.1.1. A relatív mozgás elve................................................................... 133 3.1.2. A relatív mozgás matematikai modellje ....................................... 135 3.2. Vektor abszolút és helyi deriváltja .......................................................... 137 3.3. Anyagi pont relatív kinematikája............................................................. 138 3.3.1. Anyagi pont pályája a relatív mozgásban .................................... 138 A. Vektormódszer ............................................................................. 138 B. Mátrixmódszer .............................................................................. 141 3.3.2. Anyagi pont sebessége a relatív mozgásban.............................. 143 A. Vektormódszer ............................................................................. 143 B. Mátrixmódszer .............................................................................. 144 3.3.3. Anyagi pont gyorsulása a relatív mozgásban.............................. 146 A. Vektormódszer ............................................................................. 146 B. Mátrixmódszer .............................................................................. 147 3.4. Anyagi test relatív kinematikája .............................................................. 151 3.4.1. Anyagi test közvetített mozgásának sajátosságai ....................... 151 3.4.2. Anyagi test adott pontjának pályái a relatív mozgásban ............. 152 3.4.3. Anyagi test adott pontjának sebessége a relatív mozgásban ..... 153 A. Vektormódszer ............................................................................. 153 B. Mátrixmódszer .............................................................................. 155 3.4.4. Anyagi testpont gyorsulása a relatív mozgásban ........................ 159 A. Vektormódszer ............................................................................. 159 B. Mátrixmódszer .............................................................................. 161 Függelék ........................................................................................................ 165 Irodalom......................................................................................................... 169 Kinematics (Summary) .................................................................................. 171 Contents......................................................................................................... 172 Kinematik (Zusammenfassung) ..................................................................... 176 Inhalt .............................................................................................................. 177 Cinematică (Rezumat) ................................................................................... 181 Cuprins........................................................................................................... 182 hu_HU
dc.description.tableofcontents Foreword ............................................................................................................9 CHAPTER I. KINEMATICS OF THE MATERIAL POINT 1.1. Basic concepts..........................................................................................11 1.2. Kinematic parameters of the material point ..............................................12 1.2.1. Trajectory of material point.............................................................12 1.2.2. Velocity of material point ................................................................12 1.2.3. Acceleration of material point.........................................................14 1.2.4. The calculus of components of the acceleration vector.................16 1.2.5. Geometric application ....................................................................17 1.3. Kinematics of material point in polar coordinates .....................................18 1.3.1. The peculiarities of the motion in polar coordinates.......................18 1.3.2. The velocity in polar coordinates....................................................20 1.3.3. The acceleration in polar coordinates ............................................20 1.3.4. The vectorization of the angular velocity........................................22 CHAPTER II. KINEMATICS OF THE RIGID BODY 2.1. Basic concepts..........................................................................................23 2.2. Simple motions .........................................................................................24 2.2.1. The translatory motion ...................................................................24 A. Vector method ................................................................................24 B. Matrix method .................................................................................26 2.2.2. The rotation over a fixed axis .........................................................28 A. Vector method ................................................................................ 28 2.2.2.1. The repartition of velocities ...................................................... 29 2.2.2.2. The repartition of accelerations ................................................ 31 B. Matrix method................................................................................. 34 2.2.2.3. The matrix interpretation of the motion law .............................. 34 2.2.2.4. The matrix form of the velocity ................................................. 36 2.2.2.5. The matrix form of the acceleration.......................................... 37 2.3. Compound motions................................................................................... 39 2.3.1. The helical motion.......................................................................... 39 A. Vector method ................................................................................ 40 2.3.1.1. The repartition of velocities ...................................................... 41 2.3.1.2. The repartition of accelerations ................................................ 43 B. Matrix method................................................................................. 46 2.3.1.3. The matrix model of the motion................................................ 46 2.3.1.4. The matrix form of the velocity ................................................. 47 2.3.1.5. The matrix form of the acceleration.......................................... 49 2.3.2. The plane motion ........................................................................... 51 A. Vector method ................................................................................ 53 2.3.2.1. The repartition of velocities ...................................................... 53 2.3.2.2. The instantaneous pole of velocities ........................................ 57 2.3.2.3. The centroids of the motion...................................................... 58 2.3.2.4. Practical applications................................................................ 60 2.3.2.5. Graphic methods ...................................................................... 61 2.3.2.6. The repartition of accelerations ................................................ 63 2.3.2.7. The instantaneous pole of accelerations.................................. 64 2.3.2.8. The peculiarities of the acceleration......................................... 65 2.3.2.9. The geometric aspect of the acceleration ................................ 67 B. Matrix method................................................................................. 69 2.3.2.10. The repartition of velocities using matrices ............................ 69 2.3.2.11. The matrix form of the centroids............................................. 71 2.3.2.12. The reciprocal enveloping of the centroids ............................ 73 2.3.2.13. The repartition of accelerations using matrices...................... 75 2.3.2.14. The pole of accelerations ....................................................... 76 2.3.3. The spherical motion...................................................................... 77 2.3.3.1. Definition of the spherical motion ............................................. 77 2.3.3.2. The degrees of freedom of a rigid body by spherical motion ... 79 2.3.3.3. The equations of the trajectories by spherical motion.............. 80 A. General definition ........................................................................... 80 B. Discussion on trajectories using Euler’s angles ............................. 81 C. Discussion on trajectories using elementary rotations................... 83 2.3.3.4. The repartition of velocities ...................................................... 84 A. Vector method ................................................................................ 84 B. Matrix method................................................................................. 87 2.3.3.5. The axode surfaces.................................................................. 91 2.3.3.6. The repartition of accelerations ................................................ 93 A. Vector method ................................................................................93 B. Matrix method .................................................................................97 2.3.3.7. The study of the pole of accelerations....................................100 2.3.4. The general motion ......................................................................102 2.3.4.1. Definition of the general motion..............................................102 2.3.4.2. The equations of the trajectory of an arbitrary point ..............105 A. Vector method ..............................................................................105 B. Matrix method ...............................................................................107 2.3.4.3. The repartition of velocities.....................................................109 A. Vector method ..............................................................................109 B. Matrix method ...............................................................................112 2.3.4.4. The existence of the instantaneous axis of rotation ...............115 2.3.4.5. The instantaneous axis of helical motion ...............................120 2.3.4.6. The repartition of accelerations ..............................................126 A. Vector method ..............................................................................126 B. Matrix method ...............................................................................127 2.3.4.7. The pole of accelerations .......................................................129 CHAPTER III. THE RELATIVE MOTION 3.1. Definition of the relative motion ..............................................................133 3.1.1. The principle of the relative motion ..............................................133 3.1.2. The mathematic model of the relative motion ..............................135 3.2. The local and the absolute derivative of a vector ...................................137 3.3. The relative kinematics of the material point ..........................................138 3.3.1. The trajectory of the material point executing a relative motion ..138 A. Vector method ..............................................................................138 B. Matrix method ...............................................................................141 3.3.2. The velocity of the material point executing a relative motion .....143 A. Vector method ..............................................................................143 B. Matrix method ...............................................................................144 3.3.3. The acceleration of the material point by relative motion ............146 A. Vector method ..............................................................................146 B. Matrix method ...............................................................................147 3.4. The relative kinematics of the rigid body ................................................151 3.4.1. Peculiarities of the relative motion of a rigid body........................151 3.4.2. The trajectories of a point on the rigid body by relative motion..........152 3.4.3. The velocity of a point of the rigid body by relative motion ................153 A. Vector method ..............................................................................153 B. Matrix method ...............................................................................155 3.4.4. The acceleration of a point of the rigid body by relative motion .........159 A. Vector method .............................................................................. 159 B. Matrix method............................................................................... 161 Appendix........................................................................................................ 165 Bibliography ................................................................................................... 169 Kinematics (Summary) .................................................................................. 171 Kinematik (Zusammenfassung) ..................................................................... 176 Inhalt .............................................................................................................. 177 Cinematică (Rezumat) ................................................................................... 181 Cuprins........................................................................................................... 182 en
dc.description.tableofcontents Cuvânt înainte .................................................................................................... 9 CAPITOLUL I. CINEMATICA PUNCTULUI MATERIAL 1.1. Noţiuni fundamentale ................................................................................11 1.2. Parametrii cinematici ai punctului material ...............................................12 1.2.1. Traiectoria punctului material .........................................................12 1.2.2. Viteza punctului material ................................................................12 1.2.3. Acceleraţia punctului material ........................................................14 1.2.4. Calculul componentei normale şi tangenţiale ale acceleraţiei .......16 1.2.5. Aplicaţie geometrică.......................................................................17 1.3. Cinematica punctului material în coordonate polare ................................18 1.3.1. Particularităţile mişcării în coordonate polare ................................18 1.3.2. Viteza punctului material în coordonate polare..............................20 1.3.3. Acceleraţia punctului material în coordonate polare ......................20 1.3.4. Vectorizarea vitezei unghiulare......................................................22 CAPITOLUL II. CINEMATICA RIGIDULUI 2.1. Noţiuni fundamentale ................................................................................23 2.2. Mişcări simple ...........................................................................................24 2.2.1. Mişcarea de translaţie ....................................................................24 A. Metoda vectorială ...........................................................................24 B. Metoda matriceală ..........................................................................26 2.2.2. Mişcarea de rotaţie cu axă fixă ......................................................28 A. Metoda vectorială ........................................................................... 28 2.2.2.1. Repartiţia de viteze................................................................... 29 2.2.2.2. Repartiţia de acceleraţii............................................................ 31 B. Metoda matriceală .......................................................................... 34 2.2.2.3. Interpretarea matriceală a legii de mişcare .............................. 34 2.2.2.4. Forma matriceală a vitezei ....................................................... 36 2.2.2.5. Forma matriceală a acceleraţiei ............................................... 37 2.3. Mişcări compuse....................................................................................... 39 2.3.1. Mişcarea elicoidală ........................................................................ 39 A. Metoda vectorială ........................................................................... 40 2.3.1.1. Repartiţia de viteze................................................................... 41 2.3.1.2. Repartiţia de acceleraţii............................................................ 43 B. Metoda matriceală .......................................................................... 46 2.3.1.3. Modelul matriceal al mişcării elicoidale .................................... 46 2.3.1.4. Forma matriceală a vitezei ....................................................... 47 2.3.1.5. Forma matriceală a acceleraţiei ............................................... 49 2.3.2. Mişcarea plan-paralelă................................................................... 51 A. Metoda vectorială ........................................................................... 53 2.3.2.1. Repartiţia de viteze................................................................... 53 2.3.2.2. Polul vitezelor ........................................................................... 57 2.3.2.3. Centroidele mişcării plan-paralele............................................ 58 2.3.2.4. Aplicaţii tehnice ........................................................................ 60 2.3.2.5. Metode grafice.......................................................................... 61 2.3.2.6. Repartiţia de acceleraţii............................................................ 63 2.3.2.7. Polul acceleraţiilor .................................................................... 64 2.3.2.8. Proprietăţile acceleraţiei ........................................................... 65 2.3.2.9. Interpretarea geometrică a acceleraţiei.................................... 67 B. Metoda matriceală .......................................................................... 69 2.3.2.10. Tratarea matriceală a repartiţiei de viteze.............................. 69 2.3.2.11. Forma matriceală a centroidelor............................................. 71 2.3.2.12. Înfăşurarea reciprocă a centroidelor ...................................... 73 2.3.2.13. Calculul matriceal al repartiţiei de acceleraţii ......................... 75 2.3.2.14. Polul acceleraţiilor .................................................................. 76 2.3.3. Mişcarea cu punct fix ..................................................................... 77 2.3.3.1. Definiţia mişcării cu punct fix .................................................... 77 2.3.3.2. Gradele de libertate în mişcarea cu punct fix........................... 79 2.3.3.3. Ecuaţiile traiectoriilor în mişcarea cu punct fix ......................... 80 A. Formularea generală a problemei .................................................. 80 B. Tratarea curbelor-traiectorie cu unghiurile lui Euler ....................... 81 C. Tratarea curbelor-traiectorie cu rotaţii elementare......................... 83 2.3.3.4. Repartiţia de viteze................................................................... 84 A. Metoda vectorială ........................................................................... 84 B. Metoda matriceală .......................................................................... 87 2.3.3.5. Suprafeţele axoide.................................................................... 91 2.3.3.6. Repartiţia de acceleraţii............................................................ 93 A. Metoda vectorială ...........................................................................93 B. Metoda matriceală ..........................................................................97 2.3.3.7. Studiul polului acceleraţiilor ....................................................100 2.3.4. Mişcarea generală a rigidului .......................................................102 2.3.4.1. Interpretarea mişcării generale...............................................102 2.3.4.2. Ecuaţiile traiectoriei unui punct dat al rigidului .......................105 A. Metoda vectorială .........................................................................105 B. Metoda matriceală ........................................................................107 2.3.4.3. Repartiţia de viteze.................................................................109 A. Metoda vectorială .........................................................................109 B. Metoda matriceală ........................................................................112 2.3.4.4. Condiţia existenţei axei instantanee de rotaţie.......................115 2.3.4.5. Axa instantanee de şurub.......................................................120 2.3.4.6. Repartiţia de acceleraţii ..........................................................126 A. Metoda vectorială .........................................................................126 B. Metoda matriceală ........................................................................127 2.3.4.7. Polul acceleraţiilor...................................................................129 CAPITOLUL III. MIŞCAREA RELATIVĂ 3.1. Definirea mişcării relative........................................................................133 3.1.1. Principiul mişcării relative.............................................................133 3.1.2. Modelul matematic al mişcării relative .........................................135 3.2. Derivata locală şi absolută a unui vector ................................................137 3.3. Cinematica relativă a punctului material .................................................138 3.3.1. Traiectoria punctului în mişcarea relativă ....................................138 A. Metoda vectorială .........................................................................138 B. Metoda matriceală ........................................................................141 3.3.2. Viteza punctului material în mişcarea relativă..............................143 A. Metoda vectorială .........................................................................143 B. Metoda matriceală ........................................................................144 3.3.3. Acceleraţia punctului material în mişcarea relativă......................146 A. Metoda vectorială .........................................................................146 B. Metoda matriceală ........................................................................147 3.4. Cinematica relativă a rigidului .........................................................151 3.4.1. Particularităţile mişcării relative a rigidului ...................................151 3.4.2. Traiectoriile punctului oarecare al rigidului în mişcarea relativă ..152 3.4.3. Viteza unui punct oarecare al rigidului în mişcarea relativă.........153 A. Metoda vectorială .........................................................................153 B. Metoda matriceală ........................................................................155 3.4.4. Acceleraţia unui punct oarecare al rigidului în mişcarea relativă.159 A. Metoda vectorială ......................................................................... 159 B. Metoda matriceală ........................................................................ 161 Anexă............................................................................................................. 165 Bibliografie ..................................................................................................... 169 Kinematics (Summary) .................................................................................. 171 Contents......................................................................................................... 172 Kinematik (Zusammenfassung) ..................................................................... 176 Inhalt .............................................................................................................. 177 Cinematică (Rezumat) ................................................................................... 181 ro_RO
dc.format PDF hu_HU
dc.format.medium paper hu_HU
dc.language.iso hun hu_HU
dc.rights Máté, Márton hu_HU
dc.subject Kinematika hu_HU
dc.subject műszaki tudományok hu_HU
dc.subject mechanika hu_HU
dc.title Műszaki mechanika – kinematika hu_HU
dc.type Book hu_HU
europeana.provider Erdélyi Múzeum-Egyesület hu_HU
europeana.type IMAGE hu_HU


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