Syllabus
Syllabus for PHY4222 Fall 2022 is available in pdf format here.
Syllabus for PHY4222 Fall 2022 is available in pdf format here.
| Date | Notes | Zoom Link |
| Wednesday 8/24 | Introductions, course policies. Syllabus.
Textbook: John R. Taylor "Classical Mechanics" Action item for students who did not take PHY3221 at UF: Look at the schedule from Mechanics I and review which sections from the book have been covered so far. |
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| Friday 8/26 | Review of the Newtonian and the Lagrangian formulation of Mechanics. Generalized coordinates. | |
| Monday 8/29 | Reading material: sections 13.1, 13.2. Hamiltonian formulation of mechanics. Configuration space, state space and phase space. Generalized momenta. Solving for the generalized velocities in terms of the generalized momenta. Hamiltonian. Hamilton's equations. The procedure for deriving Hamilton's equations of motion (page 532) and illustrative examples: Example 13.1 A bead on a straight wire. |
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| Wednesday 8/31 | Reading material: sections 13.3, 13.4. More examples: Example 13.2 Atwood's machine. Example 13.3 Hamilton's equations for a particle in a central force field. Example 13.4 Hamilton's equations for a mass on a cone. |
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| Friday 9/2 | Reading material: sections 13.5, 13.6. Problem 13.10.
Section 13.6. Phase-space orbits. Section 13.4 Ignorable
coordinates and conserved quantities. Problem 13.22. Section 13.5 Lagrange vs Hamilton. Canonical transformations. Problem 13.25. Example 13.5 One-dimensional harmonic oscillator. Phase space orbits. Problem 13.12: an example of a Hamiltonian not equal to the energy. |
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| Monday 9/5 | LABOR DAY- no class. | |
| Wednesday 9/7 | Homework 1 due today. Quiz. Examples of Liouville's theorem. Harmonic oscillator. Example 13.6 A falling body (see also Problem 13.2) |
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| Friday 9/9 | Begin Chapter 8. Reading material: Sections 8.1, 8.2 and 8.3 Formulation of the problem. Center of mass and relative coordinates. Separation of variables (see Problem 8.1). Reduced mass (See Problem 8.4). The equations of motion. CM frame. | |
| Monday 9/12 | Chapter 8. Reading material: Section 8.4. Section 8.4: The equivalent one-dimensional problem. Centrifugal force and centrifugal potential energy. Energy considerations. Effective potential energy. Bounded and unbounded orbits. |
9/12 |
| Wednesday 9/14 | Chapter 8. Reading material: Section 8.5. Quiz Section 8.5: Derivation of the equation of the orbit. Example 8.3: The radial equation for a free particle. Bounded orbits: aphelion, perihelion, Eccentricity. Pf. ellipses are solutions to radial eqn. |
9/14 |
| Friday 9/16 | Chapter 8. Reading material: Sections 8.6-8.8. Section 8.7: Unbounded Kepler orbits. Problem 8.30. Properties of parabolas and hyperbolas. Conic sections. The orbital period: Kepler's third law. Relation between energy and eccentricity. |
9/16 |
| Monday 9/19 | Homework 2 due today.
Examples. Three-body problem & restricted three-body problem. Lagrange points. |
9/19 |
| Wednesday 9/21 | Chapter 12. Reading material: Sections 12.1, 12.2, 12.3. Definition of chaos. Uncertainty in the initial conditions. Examples of chaotic systems. The necessary conditions for chaotic behavior: non-linearity and complexity. Section 12.1: Linearity and non-linearity. Superposition principle. Section 12.2: The Driven Damped Pendulum. Section 12.3: 1) The linear oscillator; 2) The nearly linear oscillations; 3) Appearance of harmonics of the drive frequency. | |
| Friday 9/23 | Reading material: Section 12.9. Quiz The logistic map (read only up to and including page 506). Maps versus functions. Examples: quadratic function; exponential function or multiplicative map (exponential growth). The logistic map.The carrying capacity of the model. Fixed points. Graphical representation. The fixed points of the logistic map. Test for the stability of a fixed point. Geometrical interpretation. Cool videos and demos: Chaos in the double pendulum Chaos in the double pendulum illuminated Rabbits and foxes Fractals from chaos Why do colliding blocks compute pi? |
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| Monday 9/26 | Begin Chapter 9. Section 9.1. Acceleration without rotation. | |
| Wednesday 9/28 | Hurricane day | |
| Friday 9/30 | Hurricane day | |
| Monday 10/3 | Homework 3 due today.
Review session in preparation for the first exam. covers Chapters 8, 12 and 13. |
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| Wednesday 10/5 | First Midterm Exam.
Exam covers Chapters
8,12,13. |
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| Friday 10/7 | Homecoming - no class. | |
| Monday 10/10 | Review of the solutions to the first exam (if
needed). Example 9.1: Pendulum in an accelerating car. Effective gravity. Section 9.2. The Tides. Qualitative explanation of the tides. Tidal effect due to the Moon and the Sun. Spring tides and neap tides. Finish Section 9.2. Quantitative discussion. Tidal force. Magnitude of the tides. |
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| Wednesday 10/12 | Section 9.3 "The Angular
Velocity Vector". Optional term paper prospectus due; see syllabus. Angular velocity vector. The useful relation (9.22). Addition of angular velocities. Notation for angular velocities. Time derivatives in a Rotating Frame. |
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| Friday 10/14 | Newton's second law in a rotating frame. Coriolis force and centrifugal force. (Problem 9.10: azimuthal force.) Section 9.6. The centrifugal force. Order of magnitude comparison of the Coriolis and centrifugal forces. Free-fall acceleration and the plumb line. | 10/14 |
| Monday 10/17 | Section 9.7 The Coriolis Force. Direction of the Coriolis force. Problem 9.8. Problem 9.16. Example 9.2: Simple motion on a turntable. Section 9.8: Free fall and the Coriolis force. |
10/17 |
| Wednesday 10/19 | Quiz.
Examples. Deflection of falling object by Coriolis force. Section 9.9. The Foucault Pendulum. Section 9.10. Coriolis force and Coriolis acceleration. |
10/19 |
| Friday 10/21 | Homework 4 due today.
Begin Chapter 10. Rotational motion of rigid bodies. Section 10.1 Properties of the center-of-mass (CM). The total momentum and the CM. The total angular momentum. Kinetic energy. Potential energy of a rigid body. Section 10.2. Rotation about a fixed axis. Moment of inertia. Products of inertia. |
10/21 |
| Monday 10/24 | Section 10.3. Rotation about any axis: the inertia tensor. The system of equations (10.36) relating the compoinents of the angular momentum and the components of the angular velocity. Symmetry property of the inertia tensor. Calculating moments of inertia and products of inertia. Eigenvalues of the inertia tensor. Diagonalization of the inertia tensor. Example 10.1. | |
| Wednesday 10/26 | Section 10.4: Principal axes of
inertia. Quiz Existence of Principal Axes theorem. Examples 10.2 and 10.3. Problem 10.26. 10.4: Principal axes of a cube. Diagonalization of the inertia tensor. |
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| Friday 10/28 | Sections 10.5,10.6. Invariance of inertia tensor of a cube w/ axis through CM to rotations. Torsional oscillations of a cube around different axes. Heuristic discussion of rotations. Precession and nutation of a top. Note: we are skipping sections 10.7-10.10. For those who need a refresher on linear algebra, see the series by 3blue1brown, in particular eigenvectors and eigenvalues (chapter14). | |
| Monday 10/31 | Homework 5 due today.
Begin Chapter 11. Coupled Oscillators and Normal Modes. Section 11.5. The general case. |
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| Wednesday 11/2 | Section 11.1. Two masses and three springs. Section 11.2. Identical springs and equal masses. Normal coordinates (see problem 11.9). Problem 11.27. | |
| Friday 11/4 | Quiz Section 11.3. Two weakly coupled oscillators. Electrical circuits analogy |
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| Monday 11/7 |
Quiz Section 11.4. Lagrangian approach: the double pendulum. |
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| Wednesday 11/9 | Double pendulum. Begin Chapter 14. Scattering experiments in high energy physics. The need for probabilistic description. | |
| Friday 11/11 | Veteran's day - no class. | |
| Monday 11/14 | Homework 6 due today. Continue with Chapter 14. Section 14.1. The scattering angle and impact parameter. Section 14.2 The collision cross-section. Example 14.1 Shooting crows in a tree. Section 14.3. Generalizations of the cross-section. Elastic versus inelastic cross-sections. Various types of inelastic processes: ionization, capture, fission. |
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| Wednesday 11/16 | Section 14.4. The Differential
scattering cross-section. Solid angle. Example
14.4. Section 14.5 Calculating the differential cross-section. Hard sphere scattering. |
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| Friday 11/18 | Section 14.6. Differential scattering x-section for Rutherford scattering. Experimental verification and proof of existence of nucleus. | 11/18 |
| Monday 11/21 | Difference between scattering x-section in CM and lab frames. Begin Ch. 16. Derivation of wave equation on a string. | 11/21 |
| Wednesday 11/23 | Thanksgiving holiday - no class. | |
| Friday 11/25 | Thanksgiving
holiday - no class. |
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| Monday 11/28 | Homework 7 due today. Review for second exam | |
| Wednesday 11/30 | Second midterm exam The exam covers Chapters 9, 10, 11 and 14 | |
| Friday 12/2 | Optional term papers due. Discussion of 2nd exam. Evolution of a triangular pulse. Standing wave (end of Sec. 16.2). Section 16.3: Boundary conditions; waves on a finite string. Normal modes. Fundamental frequency. Harmonics. Section 16.4: The three-dimensional wave equation. The Laplacian. Plane waves and spherical waves. | |
| Monday 12/5 | Quiz. Chapter 15. Special relativity. Lorentz transformation. Current, velocity and momentum 4-vectors. 4-tensors. | |
| Wednesday 12/07 | Homework 8 due today.Four-vectors. The invariant scalar product. Electrodynamics and relativity.Invariance of the interval. More spacetime geometry. Minkowski diagrams; spacelike, timelike and lightlike intervals. Ladder-barn paradox. Relativistic kinematics. | |
| Wednesday 12/14 | Final exam in class 10am-12pm |
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Last Updated: 13-Aug-22
Questions, comments on web site to P.J. Hirschfeld:
pjh@phys.ufl.edu