Introductions, course policies. Syllabus. Textbook: John R. Taylor "Classical Mechanics"
Action items for the students who were not in the Mechanics I class last semester:
1. Look at the diary from Mechanics I and review which sections from the book have been covered so far.
2. Inspect the PHY4222 course website on canvas (to appear) and review the sample test and the sample quiz from last semester.
3. Inspect the PHY4222 course website on canvas (to appear) and review the two Mathematica notebooks discussed in class on December 4 and 6 last semester.
|Wednesday 1/10||(no quiz today) Review of the Newtonian and the Lagrangian formulation of Mechanics. Generalized coordinates.|
Reading material: section 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.
|Monday 1/15||MLK Day - no class.|
no quiz today
Reading material: section 13.3.
The procedure for deriving Hamilton's equations of motion (page 532) and illustrative examples:
Example 13.1 A bead on a straight wire.
Example 13.2 Atwood's machine.
Example 13.3 Hamilton's equations for a particle in a central force field. See also Problem 13.19.
Example 13.4 Hamilton's equations for a mass on a cone.
Section 13.6. Phase-space orbits.
Example 13.5 One-dimensional harmonic oscillator.
Phase space orbits. Examples of Liouville's theorem.
Example 13.6 A falling body (see also Problem 13.2).
Section 13.4 Ignorable coordinates and conserved quantities. Problem 13.22.
Section 13.5 Lagrange vs Hamilton.
Homework 1 due today.
Begin Chapter 8. Reading material: Section 8.1 and 8.2. Formulation of the problem. Center of mass and relative coordinates.
|Friday 1/26||Chapter 8. Reading material: Section 8.3. Separation of variables (see Problem 8.1). Reduced mass (See Problem 8.4). The equations of motion. CM frame.|
|Monday 1/29||Chapter 8. Reading material: Section 8.4. The equivalent one-dimensional problem. Centrifugal force and centrifugal potential energy. Energy considerations. Effective potential energy. Bounded and unbounded orbits.|
|Wednesday 1/31||(no quiz day) Chapter 8. Reading material: Section 8.5 and 8.6. Derivation of the equation of the orbit. Example 8.3: The radial equation for a free particle. The Kepler orbits. Bounded and unbounded orbits.|
|Friday 2/2||Finish Section 8.6. Problem 8.16. Bounded orbits: aphelion, perihelion, properties of an ellipse. Eccentricity. The orbital period: Kepler's third law. Relation between energy and eccentricity. Unbounded Kepler orbits. Problem 8.30. Properties of parabolas and hyperbolas. Conic sections.|
Homework 1 due today.
Reading material: Section 12.9. The logistic map.
|Wednesday 2/7||quiz day! 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 DDP. Section 12.3: 1) The linear oscillator; 2) The nearly linear oscillations; 3) Appearance of harmonics of the drive frequency.|
|Friday 2/9||Illustrations of orbits for central force motion. Phase space orbits.|
|Monday 2/12||Review session in preparation for the first exam. Overview of the two quizzes. The exam covers Chapters 8, 12 and 13. In particular: Sections 8.1-8.7 (skip 8.8); Sections 12.1-12.3 and 12.9 (skip the rest); Sections 13.1-13.6 (skip 13.7).|
|Wednesday 2/14||Periodic testing: first midterm exam The exam will cover Chapters 8, 12 and 13.|
|Friday 2/16||Review of the solutions to the first exam. Begin Chapter 9. Section 9.1. Acceleration without rotation. Example 9.1: Pendulum in an accelerating car. Effective gravity.|
|Monday 2/19||Section 9.2. The Tides. Qualitative explanation of the tides. Tidal force. Magnitude of the tides. Tidal effect due to the Moon and the Sun. Spring tides and neap tides.|
|Wednesday 2/21||no quiz today|
|Wednesday 2/28||quiz day!|
|Monday 3/5||Spring Break - no class.|
|Wednesday 3/7||Spring Break - no class.|
|Friday 3/9||Spring Break - no class.|
|Wednesday 3/14||no quiz today|
|Monday 3/19||Review session in preparation for the second exam.|
|Wednesday 3/21||Periodic testing: second exam|
|Friday 3/23||Review of the solutions to the second exam.|
|Wednesday 3/28||no quiz today|
|Wednesday 4/4||quiz day!|
|Wednesday 4/11||quiz day!|
|Monday 4/16||Review session in preparation for the third exam.|
|Wednesday 4/18||KM out of town|
|Friday 4/20||KM out of town|
|Monday 4/23||Periodic testing: third exam|
|Wednesday 4/25||Review of the solutions to the third exam.|