| |
Description: Mastery of classical mechanics is integral to the advanced study of physics and engineering. Classical Mechanics with MATLAB Applications is an essential resource for the undergraduate course in classical mechanics. Filled with comprehensive examples and thorough descriptions, this text guides students through the complex topics of rigid body motion, moving coordinate systems, Lagrangian dynamics, small vibrations, the Euler algorithm, and much more. Step-by-step illustrations, examples, and computational physics tools further enhance learning and understanding by demonstrating accessible ways of obtaining mathematical solutions. Each chapter also contains a section of MATLAB code to introduce programming scripts and modification of these scripts for the reproduction of graphs and simulations.
Key features:
• Provides a review of Newton’s laws, harmonic motion, motion beyond one dimension, vector calculus, systems of coordinates, central forces, and much more!
• Features the popular numerical Euler algorithm from the start and uses the more sophisticated Runge-Kutta method of solving differential equations in later chapters.
• Includes MATLAB scripts that become increasingly sophisticated with more advanced topics, such as binary systems, rocket motion, motion of rigid bodies, and Lagrangian dynamics.
• Includes a MATLAB tutorial in Appendix A.
• An Instructor’s Solutions Manual and complete Java source code are available online.
Contents:
Chapter 1: Review of Newton’s Laws • Introduction • Basic ideas of Newton’s Laws of Motion • Numerical applications of Newton’s Second law using the modified Euler method • Chapter 1 Problems
Chapter 2: Application of Newton’s 2nd Law of Motion in One Dimension • Introduction • Constant force • Time-dependent force • Position-dependent force • Velocity-dependent force • Chapter 2 Problems
Chapter 3: Harmonic Motion in One Dimension • Introduction • Hooke’s law and the simple harmonic oscillator • Small oscillatons and the potential energy function • The harmonic oscillator with damping • The forced harmonic oscillator with dampingChapter 4: Examples of Harmonic Motion • Introduction • The simple pendulum • The physical pendulum • The bobbing buoy • The elongating wire • The torsional pendulum • The parallel beam under a shearing stress • The floating sphere • The wire under tension • The RLC circuit • The hanging spring-mass system and the spring mass correction • Springs in series and in parallel • Interacting spring-mass systems • The method of successive approximations • Beyond the linear approximation: Two examples • Chapter 4 Problems
Chapter 5: Vectors and Differential Calculus • Introduction • Vector addition and substraction • Vector multiplication • Coordinate system transformations • Vector derivatives, relative displacement and velocity • Gradient, divergence and curl • Chapter 5 problems
Chapter 6: Motion in Two and Three Dimensions • Introduction • Uncoupled or separable forces • Potential energy function • Two-dimensional motion of a charged particle in an electromagnetic field • Three-dimensional motion of a charged particle in an electromagnetic field • Chapter 6 problems
Chapter 7: Systems of Coordinates • Introduction • Plane polar coordinates • Cylindrical polar coordinates • Spherical polar coordinates • Moving coordinate systems • Rotating coordinate systems • Applications to the rotating Earth • The Foucault Pendulum • Chapter 7 problems
Chapter 8: Central Forces • Introduction • Central forces and potential energy • Angular momentum of a central force system • Total energy and central forces • The equation for r(0) • General inverse squared force • Kepler’s Laws • Orbit transfers • Oscillations about Circular orbits • Chapter 8 problems
Chapter 9: Gravitation • Gravitational force and gravitational field • Gravitational potential energy and gravitational potential • Examples on gravitation
Chapter 10: Rutherford Scattering • Introduction • Coulomb’s Law and a charge’s motion under repulsive electric force • Simulation of an alpha particle incident on a heavy target • Chapter 10 problems
Chapter 11: Systems of Particles • Introduction • Centre of mass and center of gravity • Multiparticle systems • Variable mass rocket motion • Rocket takeoff from the surface of a massive body-motion simulation • Center of mass frame revisited • Collisions • Rutherford scattering revisited • Chapter 11 problems
Chapter 12: Motion of Rigid Bodies • Introduction • Center of mass • Angular momentum, moment of inertia, inertia tensor and torque • Further inertia properties • Kinetic energy • Euler’s equations • Eulerian angles • Chapter 12 problemsChapter 13: Lagrangian Dynamics • Introduction • Generalized coordinates • Generalised Forces • Lagrange’s equations • Generalized momentum and ignorable coordinates • More examples of Lagrange’s equations • Hamilton’s Equations • Hamilton’s variational principle of least action and simulation • Chapter 13 Problems
Appendix A: MATLAB tutorial • Appendix B: Useful mathematics formulas used in the text • Appendix C: Plane geometry • One, two, three-dimensional elements • Answers to selected problems • References • IndexISBN - 9789380108162
|
| |
Pages : 576
|