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El. knyga: Elementary Mechanics Using Matlab: A Modern Course Combining Analytical and Numerical Techniques

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Elementary Mechanics Using Matlab: A Modern Course Combining Analytical and Numerical TechniquesDidesnis paveikslėlis
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This book – specifically developed as a novel textbook on elementary classical mechanics – shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks.

Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts.

While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Matlab, and a chapter devoted to the basics of scientific programming with Matlab is included. A parallel edition using Python instead of Matlab is also available.

Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.

1 Introduction 1(8)
1.1 Physics
1(1)
1.2 Mechanics
2(1)
1.3 Integrating Numerical Methods
3(1)
1.4 Problems and Exercises
4(1)
1.5 How to Learn Physics
5(2)
1.6 How to Use This Book
7(2)
2 Getting Started with Programming 9(22)
2.1 A Matlab Calculator
9(2)
2.2 Scripts and Functions
11(2)
2.3 Plotting Data-Sets
13(1)
2.4 Plotting a Function
14(5)
2.5 Random Numbers
19(1)
2.6 Conditions
20(1)
2.7 Reading Real Data
21(10)
2.7.1 Example: Plot of Function and Derivative
22(9)
3 Units and Measurement 31(12)
3.1 Standardized Units
31(3)
3.2 Changing Units
34(1)
3.3 Uncertainty and Significant Digits
34(2)
3.4 Numerical Representation
36(7)
4 Motion in One Dimension 43(40)
4.1 Description of Motion
44(14)
4.1.1 Example: Motion of a Falling Tennis Ball
50(8)
4.2 Calculation of Motion
58(25)
4.2.1 Example: Modeling the Motion of a Falling Tennis Ball
64(19)
5 Forces in One Dimension 83(56)
5.1 What Is a Force?
83(3)
5.2 Identifying Forces
86(2)
5.3 Newton's Second Law of Motion
88(5)
5.3.1 Example: Acceleration and Forces on a Lunar Lander
90(3)
5.4 Force Models
93(1)
5.5 Force Model: Gravitational Force
94(2)
5.6 Force Model: Viscous Force
96(7)
5.6.1 Example: Falling Raindrops
99(4)
5.7 Force Model: Spring Force
103(16)
5.7.1 Example: Motion of a Hanging Block
112(7)
5.8 Newton's First Law
119(1)
5.9 Newton's Third Law
119(20)
5.9.1 Example: Weight in an Elevator
123(16)
6 Motion in Two and Three Dimensions 139(44)
6.1 Vectors
139(7)
6.2 Description of Motion
146(14)
6.2.1 Example: Mars Express
153(7)
6.3 Calculation of Motion
160(11)
6.3.1 Example: Feather in the Wind
168(3)
6.4 Frames of Reference
171(12)
6.4.1 Example: Motion of a Boat on a Flowing River
173(10)
7 Forces in Two and Three Dimensions 183(32)
7.1 Identifying Forces
183(4)
7.2 Newton's Second Law
187(2)
7.3 Force Model—Constant Gravity
189(3)
7.3.1 Example: Motion of a Ball with Gravity
190(2)
7.4 Force Model—Viscous Force
192(5)
7.4.1 Example: Path Through a Tornado
194(3)
7.5 Force Model—Spring Force
197(7)
7.5.1 Example: Motion of a Bouncing Ball with Air Resistance
201(3)
7.6 Force Model—Central Force
204(11)
7.6.1 Example: Comet Trajectory
205(10)
8 Constrained Motion 215(14)
8.1 Linear Motion
216(1)
8.2 Curved Motion
217(12)
8.2.1 Example: Acceleration of a Matchbox Car
221(1)
8.2.2 Example: Acceleration of a Rotating Rod
222(1)
8.2.3 Example: Normal Acceleration in Circular Motion
223(6)
9 Forces and Constrained Motion 229(40)
9.1 Linear Constraints
231(7)
9.1.1 Example: A Bead in the Wind
236(2)
9.2 Force Model—Friction
238(11)
9.2.1 Example: Static Friction Forces
242(2)
9.2.2 Example: Dynamic Friction of a Block Sliding up a Hill
244(1)
9.2.3 Example: Oscillations During an Earthquake
245(4)
9.3 Circular Motion
249(20)
9.3.1 Example: A Car Driving Through a Curve
252(2)
9.3.2 Example: Pendulum with Air Resistance
254(15)
10 Work 269(34)
10.1 Integration Methods
269(3)
10.2 Work-Energy Theorem
272(3)
10.3 Work Done by One-Dimensional Force Models
275(15)
10.3.1 Example: Jumping from the Roof
281(4)
10.3.2 Example: Stopping in a Cushion
285(5)
10.4 Work Done in Two- and Three-Dimensional Motions
290(6)
10.4.1 Example: Work of Gravity
292(1)
10.4.2 Example: Roller-Coaster Motion
293(1)
10.4.3 Example: Work on a Block Sliding Down a Plane
294(2)
10.5 Power
296(7)
10.5.1 Example: Power Exerted When Climbing the Stairs
297(1)
10.5.2 Example: Power of Small Bacterium
297(6)
11 Energy 303(48)
11.1 Motivating Examples
304(5)
11.2 Potential Energy in One Dimension
309(12)
11.2.1 Example: Falling Faster
315(1)
11.2.2 Example: Roller-Coaster Motion
316(1)
11.2.3 Example: Pendulum
317(2)
11.2.4 Example: Spring Cannon
319(2)
11.3 Energy Diagrams
321(12)
11.3.1 Example: Energy Diagram for the Vertical Bow-Shot
328(2)
11.3.2 Example: Atomic Motion Along a Surface
330(3)
11.4 The Energy Principle
333(4)
11.4.1 Example: Lift and Release
334(1)
11.4.2 Example: Sliding Block
335(2)
11.5 Potential Energy in Three Dimensions
337(5)
11.5.1 Example: Constant Gravity in Three Dimensions
338(1)
11.5.2 Example: Gravity in Three Dimensions
339(1)
11.5.3 Example: Non-conservative Force Field
340(2)
11.6 Energy Conservation as a Test of Numerical Solutions
342(9)
12 Momentum, Impulse, and Collisions 351(50)
12.1 Motivating Example—Meteor Impact
352(3)
12.2 Translational Momentum
355(1)
12.3 Impulse and Change in Momentum
356(7)
12.3.1 Example: Ball Colliding with Wall
358(3)
12.3.2 Example: Hitting a Tennis Ball
361(2)
12.4 Isolated Systems and Conservation of Momentum
363(6)
12.5 Collisions
369(15)
12.5.1 Example: Ballistic Pendulum
378(2)
12.5.2 Example: Super-Ball
380(4)
12.6 Modeling and Visualization of Collisions
384(3)
12.7 Rocket Equation
387(14)
12.7.1 Example: Adding Mass to a Railway Car
390(1)
12.7.2 Example: Rocket with Diminishing Mass
390(11)
13 Multiparticle Systems 401(36)
13.1 Motion of a Multiparticle System
402(2)
13.2 The Center of Mass
404(8)
13.2.1 Example: Points on a Line
407(1)
13.2.2 Example: Center of Mass of Object with Hole
407(1)
13.2.3 Example: Center of Mass by Integration
408(2)
13.2.4 Example: Center of Mass from Image Analysis
410(2)
13.3 Newton's Second Law for Particle Systems
412(4)
13.3.1 Example: Ballistic Motion with an Explosion
413(3)
13.4 Motion in the Center of Mass System
416(2)
13.5 Energy Partitioning
418(11)
13.5.1 Example: Bouncing Dumbbell
423(6)
13.6 Energy Principle for Multi-particle Systems
429(8)
14 Rotational Motion 437(20)
14.1 Rotational State—Angle of Rotation
437(4)
14.2 Angular Velocity
441(3)
14.3 Angular Acceleration
444(1)
14.3.1 Example: Oscillating Antenna
444(1)
14.4 Comparing Linear and Rotational Motion
445(1)
14.5 Solving for the Rotational Motion
446(4)
14.5.1 Example: Revolutions of an Accelerating Disc
448(1)
14.5.2 Example: Angular Velocities of Two Objects in Contact
449(1)
14.6 Rotational Motion in Three Dimensions
450(7)
14.6.1 Example: Velocity and Acceleration of a Conical Pendulum
452(5)
15 Rotation of Rigid Bodies 457(32)
15.1 Rigid Bodies
458(1)
15.2 Kinetic Energy of a Rotating Rigid Body
458(4)
15.3 Calculating the Moment of Inertia
462(7)
15.3.1 Example: Moment of Inertia of Two-Particle System
467(1)
15.3.2 Example: Moment of Inertia of a Plate
468(1)
15.4 Conservation of Energy for Rigid Bodies
469(6)
15.4.1 Example: Rotating Rod
472(3)
15.5 Relating Rotational and Translational Motion
475(14)
15.5.1 Example: Weight and Spinning Wheel
477(3)
15.5.2 Example: Rolling Down a Hill
480(9)
16 Dynamics of Rigid Bodies 489(66)
16.1 Motivating Example—Spinning a Wheel
489(5)
16.2 Newton's Second Law for Rotational Motion
494(11)
16.2.1 Example: Torque and Vector Decomposition
498(1)
16.2.2 Example: Pulling at a Wheel
499(1)
16.2.3 Example: Blowing at a Pendulum
500(5)
16.3 Rotational Motion Around a Moving Center of Mass
505(13)
16.3.1 Example: Kicking a Ball
507(4)
16.3.2 Example: Rolling Down an Inclined Plane
511(3)
16.3.3 Example: Bouncing Rod
514(4)
16.4 Collisions and Conservation Laws
518(18)
16.4.1 Example: Block on a Frictionless Table
521(6)
16.4.2 Example: Changing Your Angular Velocity
527(2)
16.4.3 Example: Conservation of Rotational Momentum
529(2)
16.4.4 Example: Ballistic Pendulum
531(2)
16.4.5 Example: Rotating Rod
533(3)
16.5 General Rotational Motion
536(19)
Appendix A: Proofs 555(16)
Appendix B: Solutions 571(16)
Index 587
Professor Anders Malthe-Sųrenssen is a professor of physics at the University of Oslo, where his research interests are focused on the physics of geological processes.  His current teaching activity focuses on revitalizing the teaching of undergraduate science courses by seamless integration of computational methods in order to give students an early contact with research and industrially relevant problems.  
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Pastovi nuoroda: https://www.kriso.lt/db/97833191958722e.html
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