Classical Mechanics

Instructor Information

• Instructor: Dr. Chidi Okoro (Associate Professor of Physics)
• Email: cokoro@university.alkimi.ai
• Office: Meridian Science Center 412
• Office Hours:
  • Monday & Thursday: 1:00–2:30 p.m. (In person, Meridian Science Center 412)
  • Wednesday: 2:00–3:00 p.m. (Virtual via Zoom; link posted in Canvas)
  • Also available by appointment.

Course Description

Newtonian mechanics of particles and systems, oscillators, central-force motion, noninertial frames, rigid-body rotation, and the Lagrangian and Hamiltonian formulations. PHYS 310 provides an advanced, mathematically rigorous treatment of classical mechanics for upper-division physics and engineering students. Building upon multivariable calculus, linear algebra, and differential equations, we reformulate Newtonian particle dynamics into the analytical frameworks of Lagrange and Hamilton. Core topics include damped and driven harmonic oscillators, central-force orbital motion, noninertial reference frames and Coriolis effects, rigid-body tensor dynamics, coupled oscillations, and canonical Hamiltonian mechanics.

Prerequisites

PHYS 121, MATH 240, and MATH 340.

Measurable Student Learning Outcomes

Upon successful completion of PHYS 310, students will be able to:

1. Analyze Advanced Newtonian Dynamics: Formulate and solve differential equations of motion for complex single-particle and multi-particle systems subject to velocity- and position-dependent forces.
2. Evaluate Harmonic Oscillations and Phase Space: Analyze damped, driven, and resonant oscillators using Fourier techniques and construct phase-space trajectories.
3. Apply Central Force Motion and Gravitation: Derive the orbital equation for central force potentials, analyze Keplerian orbits, and calculate orbital transfers and scattering cross-sections.
4. Transform Equations in Noninertial Frames: Derive equations of motion in rotating coordinate systems, calculating centrifugal, Coriolis, and transverse Euler forces.
5. Construct Lagrangian Mechanics Formulations: Determine generalized coordinates, formulate Lagrangians, derive Euler-Lagrange equations, and identify conserved quantities using Noether's theorem.
6. Formulate Hamiltonian Dynamics and Coupled Systems: Perform Legendre transformations to construct Hamiltonians, solve canonical equations of motion, and evaluate normal modes for coupled oscillators.

Required Course Materials & Approximate Costs

1. Taylor, John R. Classical Mechanics. University Science Books, 2005. Approx. $65 for digital or paperback; approx. $95 for hardcover purchase.
2. Computational software environment (Python 3 with NumPy, SciPy, and Matplotlib). Free open-source software.
3. Total estimated cost: $65 to $95.

Generative AI Policy (AI Level 2: AI Permitted with Disclosure for Specified Tasks)

In accordance with Alkimi University Academic Policies (Student Handbook §5.8), PHYS 310 operates under AI Level 2.

• What is permitted: You may use AI tools to check intermediate differential equations, plot phase-space trajectories, clarify the Euler-Lagrange equations, or explore numerical integrations using Python or Mathematica.
• What is prohibited: You may not submit AI-generated analytical solutions or derivations for homework assignments, copy AI-written proofs, or access any generative AI or connected devices during examinations.
• Disclosure: Include a brief disclosure note at the end of each problem set stating which AI tools were consulted and the specific prompts utilized, or confirm that no AI assistance was employed.

Grading Components and Weights

• Midterm Exam 1: 20% (In class, Friday, September 25)
• Midterm Exam 2: 20% (In class, Friday, October 30)
• Weekly Analytical Problem Sets: 25% (Due Fridays at 11:59 p.m. in Canvas (weeks 2–13; lowest dropped))
• Computational Mechanics Projects: 10% (Computational Python/Jupyter modeling assignments due Wednesdays at 11:59 p.m. in Canvas)
• Final Comprehensive Examination: 25% (Tuesday, December 15, 2026, 10:30 a.m.–12:30 p.m.)

Grading Scale (Alkimi University Standard)

• A: 93–100% | A-: 90–92%
• B+: 87–89% | B: 83–86% | B-: 80–82%
• C+: 77–79% | C: 73–76% | C-: 70–72%
• D+: 67–69% | D: 60–66% | F: Below 60%
• Extra credit: No extra credit assignments are offered in PHYS 310.

Course Schedule (Fall 2026)

Course Policies

Attendance Policy

Mastering theoretical classical mechanics requires regular attendance and active engagement during classroom derivations. If an unavoidable illness or approved university event causes an absence, inform Dr. Okoro via email as soon as possible. Repeated unexcused absences will directly impair your understanding and final grade. Students who miss the first two class meetings without notifying the instructor may be dropped. Students may miss class for religious observance without penalty if they notify the instructor in writing within the first two weeks of the semester (by Wednesday, September 9, 2026). Absences for university-sponsored activities (athletics, performances, conferences) are excused with a letter from the sponsoring office at least one week in advance.

Late Work Policy

Homework submissions after the Friday deadline receive a 20% penalty per 24 hours. Because full solutions are distributed shortly after submission, no assignments will be accepted more than 24 hours late. The single lowest analytical problem set score is automatically dropped.

Final Exam Policy

The final examination (Tuesday, December 15, 2026, 10:30 a.m.–12:30 p.m.) is scheduled by the University Registrar and can't be moved without the Dean's written approval (Faculty Handbook §5.5). A student with three or more final exams on the same calendar day may reschedule one of them. Requests go to the instructor of the middle exam by the last day of classes. For this term, send the request by Wednesday, December 9, 2026 (Student Handbook §6.4).