Course Webpage for PHYS-510 (2024 Spring) at SIU--Carbondale

Course Webpage for
PHYS 510: Classical Mechanics (2024 Spring)
Department of Physics, Southern Illinois University--Carbondale
Last updated on .

General information:
- Instructor: K. V. Shajesh (Office: Neckers 491, Tel.: +1-618-453-5212)
- Class meetings: TR 9:35-10:50 AM. in Neckers 410.
- Office hours for instructor: MWF 9:30-11:00 AM; MF 4:00-5:00 PM.
- Syllabus for the course. The Provost Office has put together a Syllabus Attachment to assist the student. It lists and provides web links for many elements that are important for a student.
Resources:
- References:
  - Classical Mechanics, by Goldstein, Poole, and Safko. (Available in archive.org.)
  - Mechanics, by L.D. Landau and E.M. Lifshitz. (Available in archive.org.)
  - Mechanics, by Arnold Sommerfeld. (Available in archive.org.)
  - Mathematical Methods of Classical Mechanics, by V. I. Arnold. (Available in archive.org.)
  - Calculus of Variations, by I. M. Gelfand and S. V. Fomin. (Available in archive.org.)
- Lectures
  - Lecture recordings: 2024S [2022S, 2021S, 2020S]
  - Informal Notes: This is not a substitute for a textbook.
- Quizzes and Homework
  - Quizzes: Due in class in the beginning of the next lecture.
  - Homework: Due in Mail Box before 4:30 PM on due date.
- Exams
  - Old Exams are available in Past course webpages: [2022S, 2021S, 2020S, 2019S, 2018S, 2017S]
- Miscellaneous
  - Grades will be posted on SIU MyCourses (password protected).

COURSE CONTENT:

Newton's laws of motion: (Week 01)
1. Conservative forces
2. Position dependent forces
3. Velocity dependent forces
Resources:
Homework No. 01
Keywords: Conservative forces

Examples:
- Harmonic oscillator
- Drag forces
- Motion of a charge particle in a uniform magnetic field.
Variational principle: (Week 02, 03)
1. Functional derivative, delta function
2. Fermat's principle
3. Geodesics on surfaces
4. Brachistochrone on surfaces
Resources:
Homework No. 02
Homework No. 03
Keywords: Calculus of variations, geodesics, brachistochrone, Fermat's principle, cycloid, catenary, isochrone

Examples:
- Snell's law (Fermat's principle) for layered configurations; Mirage phenomena
- The curve of shortest distance connecting two points on a plane is a straight line, and on the surface of a sphere is a great circle.
- Brachistochrone curve
  Cycloid: A mass (perfectly) rolling on a surface in uniform gravity.
  Catenary: A rope hanging in a uniform gravity.
Stationary action principle: (Week 04)
1. Action, stationary action principle
2. Lagrangian, Euler-Lagrange equations, Newton's law for conservative forces
3. Hamiltonian, Hamilton equations of motion
Resources:
Homework No. 04
Keywords: Stationary action principle, Lagrangian, Hamiltonian, Euler-Lagrange equations, Hamilton equations of motion

Examples:
- Charged particle in electric and magnetic field
Midterm Exam No. 01 (Feb 22, Thursday).
Lagrangian mechanics: (Week 07)
1. Mechanics of objects constrained to move on surfaces
2. Equation of motion versus equation of constraint
3. Dynamical variables (generalized coordinates)
Resources:
Homework No. 05
Keywords: Lagrangian mechanics

Examples:
- Simple pendulum: An object contrained to move on a vertical circle in uniform gravity.
- Simple pendulum, with pivot constrained to move on a horizontal line.
- Inverted pendulum: A simple pendulum with pivot oscillating vertically. Horizontal oscillations do not invert the pendulum.
- Double pendulum: A simple pendulum with pivot (having mass) constrained to move on a vertical circle.
- Time period of a simple pendulum in terms of elliptic integrals.
- Cycloidal pendulum: A simple pendulum with bob constrained to move on a cycloid.
- Spherical pendulum: A simple pendulum not constrained to move in a plane.
- Foucoult pendulum: A spherical pendulum with rotation of Earth accounted.
- Marble rolling on the inside surface of a cone.
- Marble rolling on the inside surface of a hemisphere.
- Marble rolling on the inside surface of a cycloid.
Lagrangian multiplier: (Week 08)
1. Using the gradient operator to model the force of constraint.
2. Lagrangian multiplier
Resources:
Homework No. 06
Keywords: Lagrangian multiplier, D'Alembert's principle

Examples:
- Simple pendulum, spherical pendulum.
- Atwood's machine.
- Perfectly rolling wheel.
- Perfectly rolling gear configurations.
Small angle approximation: (Week 09)
1. Small angle approximation
2. Fourier transform method to solve linear differential equations
3. Normal modes
Resources:
Homework No. 07
Keywords: Normal modes, small angle approximation

Examples:
- Normal modes of two masses connected to three springs in series.
- Normal modes of a double pendulum.
- Normal modes in LC circuits.
Stationary action principle (with variations at boundary): (Week 10)
1. Generators of infinitismal transformations
2. Noether's theorem: Transformation, Symmetry, and Conservation principles.
Resources:
Homework No. 08
Keywords: Generators, Noether's theorem

Examples:
- Non-conservation principles: Virial theorems
- Boost operator
- Infinitesimal unitary transformations in quantum mechanics
Midterm Exam No. 02 (April 4, Thursday).
(Preview of) Midterm Exam No. 02
Midterm Exam No. 02
Poisson bracket: Variational calculus of dynamics (Week 11)
1. Poisson bracket
2. Generators of infinitesimal transformations
3. Statement of symmetry and transformation in terms of Poisson bracket.
Resources:
Homework No. 09
Keywords: Generators, Symmetry and transformations

Examples:
- Poisson bracket for simple and compound functions
- Poisson bracket between generators
Kepler problem (Week 13)
1. Orbit: Elliptic, parabolic, hyperbolic, circular
2. Derive Kepler's laws of planetary motion
3. Laplace-Runge-Lenz vector
4. Precession of perihelion
Resources:
Homework No. 10
Homework No. 11
Keywords: Kepler's laws

Examples:
- Elliptic orbits versus hyperbolic orbits
Special relativity (Week 15)
1. Lorentz transformation
2. Geometry of Lorentz transformation
3. Relativistic kinematics
Resources:
Homework No. 12
Keywords: Special relativity

Examples:
- Relativistic motion of an electric charge in a uniform magnetic field.
- Relativistic motion of an electric charge in a uniform electric field.
Final Exam No. (May 9, Thursday).
(Preview of) Final Exam

More information:

Evaluation:

Quiz 10% and y (required to benefit from the curve)

Homework 30%

Midterm Exams (2x20%) 40%

Final Exam 20%

Exam schedule:

Midterm Exam 1 --- Fenruary 22 (Thursday)

Midterm Exam 2 --- April 4 (Thursday)

Final Exam --- May 9 (Thursday, 2:45 PM-4:45 PM, in class)

Last updated on by K. V. Shajesh (kvshajesh@gmail.com).

Quiz	10% and y (required to benefit from the curve)
Homework	30%
Midterm Exams (2x20%)	40%
Final Exam	20%

Midterm Exam 1	---	Fenruary 22 (Thursday)
Midterm Exam 2	---	April 4 (Thursday)
Final Exam	---	May 9 (Thursday, 2:45 PM-4:45 PM, in class)