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PHY 322
Intermediate Mechanics Fall 2003 Instructor:
Valeri Petkov Text: Analytical mechanics, 6th Ed. G.R.
Fowles and G.L. Cassiday (Saunders College Publishers, Ft. Worth, 1999)
Assignments: Homework assignments will be given each week. Homeworks will be collected and graded, and solutions will be discussed in class. I encourage you to work together on the homework problems. However, homework should reflect your own effort and achievements and not be a copy of the work of others. Exams: There will be three mid-term exams and one final. Approximate dates appear in the outline below. Grading: Grades will be based on a combination of exam and homework scores. The HW will contribute a total of 25 % to the final grade. Each of the three mid-term exams will contribute 15 % and the final exam - 30 %. Grades will be based on the distribution of scores for the class. The average grade for this course in the past has been around a B-. Overview: PHY 322 builds on the material covered in PHY 145 to develop general and powerful methods for understanding and predicting the motion of physical systems. In PHY 145 you learned many of the important concepts of mechanics, like Newton's laws of motion and energy and momentum conservation. In PHY 322 you will add to this foundation by learning still more powerful mathematical techniques and more general formulations of the basic principles. A basic difference in PHY 322 is to recognize Newton's second law as a differential equation. This will allow us to study the motion of objects when the forces acting are not constant in time. One important example is the treatment of dissipative forces like air resistance. You will study problems in detail because they have many applications in physics and engineering. Among these are harmonic oscillator and the central force problem (i.e. planetary orbits). You can expect to have mastered the general solutions to such problems by the end of the semester. Finally, you will also study generalized formulations of the laws of mechanics - formulations equivalent to, but not directly involving Newton's 2nd law. The most important of these is the Lagrange formulation. While the Lagrangian does not really contain any new physics, it is very convenient to use in certain cases of problems for which F = ma is difficult to apply directly. These more general formulations also provide the foundation to quantum mechanics. As noted above, the mathematical level of this course will be higher than that of PHY 145. You will make frequent use of vector analysis and learn to solve some simple differential equations. To help with tediuos calculations, you will use Mathematica, a symbolic math software package. Mathematica is widely used in statistics, economics, and is also a very useful plotting tool. References: The following books are recommended for additional reading and study: Elementary level: "Fundamentals of Physics" - Halliday, Resnik and Walker (Wiley) Intermediate level: "Classical Dynamics of Particles and Systems" - 4th Ed. J.B. Marion and S.T. Thornton (Saunders) Advanced level: "Classical Mechanics" - H. Goldstein (Addison-Wesley) Mathematica references: Mathematica - E. Don (McGraw-Hill) WOLFRAM RESEARCH - http://www.wolfram.com/ ADA: CMU provides students with disabilities reasonable accommodation to participate in educational programs, activities and services. Students with disabilities should first register with the office of Student Disability Services and then contact me as soon as possible. Policy on Academic Integrity: In May 2001, CMU approved the Policy of Academic Integrity which applies to all students. Copies are available at: http://academicsenate.cmich.edu / All academic work is expected to be in compliance with this policy. Classroom civility: Each CMU student is encouraged
to help create an environment during class that promotes learning, dignity,
and mutual respect for everyone.
Course Outline
Classical notions of space and time (FC 1.1, 1.2) L1. Review of vectors. Vector algebra: adding, subtracting, multiplication. (FC 1.3-1.7) L2. More on vectors: cross and triple products. Derivative of a vector. (FC 1.6-1.9) L3. Vector velocity and acceleration in rectangular, cylindrical and spherical coordinates (FC 1.10-1.12) Newton's laws in one dimension Historical origins of the laws of motion (FC 2.1) L4. Constant vs. non-constant acceleration. Newton's second law as a differential Equation (FC 2.2, 2.3) L5. Position and velocity dependent forces. The concepts of Kinetics and Potential Energy. Terminal velocity. (FC 2.3,2.4) L6. Numerical treatment of Newton's second law. Using Mathematica to integrate equations of motion (FC 2.5) Oscillators R. The oscillator in Physics (FC 3.1) L7. Hooke's law and the simple harmonic oscillator (FC 3.2,3.3) L8. Damped harmonic motion: theory. Overdamped, underdamped and critically damped oscillators (FC 3.4) L9. Damped harmonic motion: applications. Setting initial conditions, integration constants and predicting future (FC 3.4,3.5) L10. Driven oscillators: theory. Inhomogeneous equations; particular and complementary solutions (FC 3.6) L11. Driven oscillators: practice. Sinusoidal and non-sinusoidal driving forces. Fourier series (FC 3.6, 3.9) L12. Non-linear oscillators and chaos. Examples of chaotic behavior (FC 3.7,3.8) L13. Exam I Motion in three dimensions R. Translating from 1-D to 3-D (FC 4.1) L14. Calculus in 3-D. Line integrals and work (FC 4.1, 4.2) L15. Projectiles. Separable forces. Range and trajectories with and without air resistance (FC 4.3) L16. Oscillators in 2-D and 3-D. Closed and open orbits (FC 4.4, 4.6) L17. Charged particles in Elector-Magnetic fields (FC 4.5) Noninertial reference systems R. Accelerated coordinate systems and Inertial forces (FC 5.1) L18. Rotating systems. Velocity and acceleration in accelerated frames (FC 5.2,5.3) L19. Earth's rotation. Static and dynamic effect. Coriolis force (FC 5.4) Gravitation and Central Forces R. Newton's universal law of gravitation (FC 6.1) L20. Gravitational force between a uniform sphere and a particle (FC 6.2) L21. Kepler's laws and the motion of the planets (FC 6.2,6.3) L22. Newton's triumph. The inverse square law. Solving the equations of motion (FC 6.3-6.6) L23. Potential energy in central force motion. Energy equation of an orbit in a central field (FC 6.6 - 6.8) L24. Motion in repulsive fields. Rutherford scattering. (FC 6.12) L25. Exam II Dynamics of systems of particles L26. Center of mass and linear momentum of a system of particles (FC 7.1) L27. Two body motion: the reduced mass (FC 7.3) L28. Collisions: elastic and inelastic (FC 7.5,7.6) L29. Motion of a body with variable mass: Rocket motion (FC 7.7) Rigid bodies: Planar motion L30. Center of mass of a rigid body. Moment of inertia (FC 8.1, 8.2) L31. The physical pendulum. Torque and inertia (FC 8.4, 8.5) L32. Laminar motion of a rigid body. Impulse and collisions. (FC 8.6, 8.7) L33. Exam III Rigid bodies: 3-D motion L34. Rotation of a rigid body about an arbitrary axis. Angular momentum and kinetic Energy (FC 9.1) L35. Principal axes: the secret of smooth rotation (FC 9.2). L36. Euler's equations of motion. Fixed and free rotation (FC 9.3, 9.4) L37. Eulerian angles: translating between the rotating body and a fixed frame (FC 9.6) L38. Gyroscopic precession: Motion of a top (FC 9.7) Lagrangian mechanics L39. Hamilton's principle (FC 10.1) L40. The Lagrange recipe. Generalized coordinates and equation of motion (FC 10.2,10.3) L41. Practice with the Lagrangian (FC 10.5) L42. The Hamiltonian (FC 10.9, 10.10) R. General Review Exam IV: Final |
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