Class Title: Mechanics I
Session: Fall 2017 (09/05/2017 – 12/12/2017)
Days & Times: Tu Th 10:00AM – 11:15AM
Location: Hasbrouck Laboratory Add room 126
Midterm Exam 1: Tuesday 10/17, 10:00AM – 11:15AM at HAS Add 126
Midterm Exam 2: Thursday 11/16, 10:00AM – 11:15AM at HAS Add 126
Final Exam: Tuesday 12/19/2017, 10:30AM – 12:30PM at HAS Add 126
Additional Honors 421 Colloquium (everybody is welcome to enroll!)
Days & Times: Mondays 6:00PM – 6:50PM
Location: Hasbrouck Laboratory Add room 126
Instructor: Tigran Sedrakyan
E-mail: tsedrakyan@physics.umass.edu
Office: HAS 105
Phone: 413-545-2409
Office hours: W 5-8pm at HAS 409. We can meet also after the lectures or other times by appointment.
TA: Guanghui Zhou
E-mail: gzhou@physics.umass.edu
Office: LGRT 1129
Office hours: Wed 2:00PM – 3:00PM
Course Description:
Newtonian dynamics and analytic methods. Conservation laws. Oscillatory phenomena including damping and resonance. Central force problems and planetary orbits. Rigid body mechanics. Introduction to the calculus of variation and the principle of least action. Generalized coordinates. Lagrangian and Hamiltonian dynamics.
Prerequisites: PHYSICS 151 or 181, MATH 233.
Textbook: Classical Dynamics of Particles and Systems (5th Edition) Paperback, Author: Jerry B. Marion by Stephen T. Thornton
Suggested reading: Mechanics: Volume 1 (Course of Theoretical Physics Series) 3rd Edition by L. D. Landau and E. M. Lifshitz.
Grading: grades from the various components of the course will determine the final grade. These are weighted as follows:
— Homework solutions — 40% (with the lowest homework grade being dropped)
— Midterm exam No 1 ( Tuesday 10/17, 10:00AM – 11:15AM at HAS Add 126, during the regular lecture hour) — 20%.
— Midterm exam No 2 ( Thursday 11/16, 10:00AM – 11:15AM at HAS Add 126, during the regular lecture hour) — 20%.
— Final exam — 20%.
(In exceptional cases when midterm and final exam scores are much higher than the homework score, the homework scores will be ignored) .
For Disability Accommodation and Academic Honesty policy statements please see:
Academic Honesty Policy Statement
Disability Statement
Where are we in the textbook? — Required reading — Homework assignments and solutions — Notes
Week 1
Matrices, Vectors, and Vector Calculus.
Required reading: Chapter 1; Example problems 1.1 through 1.8 and their solutions. See also Lecture 1 notes, and Lecture 2 notes.
Homework assignment 1 (Due Sept 14)
HW1-Solutions
Week 2
Newtonian Mechanics. Required reading: Chapter 2; Example problems 2.1 through 2.10 and their solutions. See also Lecture 3 and Lecture 4 notes.
Homework assignment 2 (Due Sept 25)
HW2 Solutions
Week 3
Motion of a particle in a magnetic field. Simple harmonic oscillator. Required reading Chapter 2 example problem 2.10, Chapter 3, paragraphs 3.1, 3.2; Example problem 3.1; and Lecture 5 notes. In Lecture 6 we discussed (i) Forced Oscillations: Beats and resonance. (ii) Damped Oscillations.
Honors section: Honors Lecture 2 notes
Homework assignment 3 (Due Sept 28)
HW3 Solutions
Week 4
We discussed Damped Oscillations, specifying underdamped, over damped, and critically damped regimes. Then considered a damped oscillator subject to a periodic force: Forced oscillations with damping (Marion paragraph 3.6), Required reading Chapter 3 paragraphs 3.3 through 3.9 (3.9 is optional). Example problems 3.2 through 3.6. Suggested reading: Chapter 5 paragraphs 21, 22 of Landau and Lifshitz (see the textbook for suggested reading).
In Lecture 8 we discussed Principle of Superposition — Fourier Series (Marion paragraph 3.8) and Conservative systems (Marion paragraphs 2.5, 2.6). Example problems 2.11, 2.12. Suggested reading: Chapter 2 paragraphs 6 through 9 of Landau Lifshitz. See also Lecture 8 notes.
Honors section: Honors Lecture 3 notes
Homework assignment 4 (Due October 5)
HW4 Solutions
Week 5
We discussed the conservation theorems. Required reading: paragraphs 2.5, 2.6.Example problems 2.11 trough 2.13. Then we discussed representations of various quantities using polar coordinates. Required reading Chapter one paragraph 1.14, 1.15. Example problem 1.8. See also Lecture 9 notes. Central-force motion. Required reading: Chapter 8 paragraphs 8.1 through 8.7. Suggested reading: Chapter 3 paragraphs 14,15 of Landau Lifshitz.
Honors section: Nonlinear oscillations, approximate solutions of equations of motion. Reading: paragraphs 4.1, 4.2. Example problem 4.1.
Homework assignment 5 (Due October 12) — Now due Friday, Oct 13.
HW5 Solutions
Week 6
No lecture on Tue, Oct 11 (because of the Columbus day holiday). Practice midterm on Thursday, Oct 12 (will not be graded). Practice Midterm: problems; solutions.
Honors section: notes of week 7.
Week 7
Midterm on Tuesday, Oct 17.
Central-force motion. Planetary motion – Kepler’s problem. Required reading: Chapter 8 paragraphs 8.1 through 8.7. Suggested reading: Chapter 3 paragraphs 14,15 of Landau Lifshitz. See also Lecture notes.
Honors section: Honors Lecture 4 and 5 notes
Required reading: Chapter 4, paragraphs 4.3 through 4.6.
Homework assignment 6 (Due October 26)
HW6: solution prob 1 and solution prob 2
Week 8
Closed orbits, small perturbations around circular orbits. Marion paragraphs 8.8, 8.9 (optional), 8.10. Example problems 8.5 through 8.7. Dynamics of a system of many particles: Center of mass, linear momentum and the energy of the system, two-body problem, scattering of two particles, totally inelastic scattering, elastic collision. Systems of many particles. Require reading: Chapter 9, paragraphs 9.1, through 9.8. Example problems 9.1 through 9.10.
Honors section: Detection of chaos by numerical analysis of differential equations.
Homework assignment 7 (Due Nov 2)
HW7 Solutions
Week 9
Dynamics of rigid bodies. Required reading: Chapter 11, paragraphs 11.1, 11.2, example problems 11.1, 11.2. Curves in higher dimensions, Functionals. Calculus of variations: Euler-Lagrange equation, Lagrangian mechanics. Required reading Chapter 6, paragraphs 6.1 through 6.4, example problems 6.1, 6.2, 6.3.
Honors Section: Scaling and Mechanical Similarity. Required reading: Landau-Lifshitz, Chapter 2 paragraph 10.
Homework assignment 8 (Due Nov 9)
HW8 Solutions
Week 10
Lagrangian mechanics/Dynamics, Generalized coordinates, Euler-Lagrange equations of motion in generalized coordinates, the principle of the least action. Required reading Chapter 6, paragraphs 6.1 through 6.4, example problems 6.1, 6.2, 6.3. Derivation of Newton’s equations of motion from Lagrangian mechanics. Required reading Required reading: Chapter 7, Chapters 7.1 through 7.4; 7.6. Small (coupled) oscillations. Two coupled harmonic oscillators, weak coupling, general problem of coupled oscillations. Required reading Chapter 12, paragraphs 12.1 through 12.4. Example problem 12.1. See also Lecture notes.
Honors section: Special cases and theorems in Lagrangian mechanics.
Week 11
Practice midterm 2: Problems and solutions
Midterm 2
Honors section: Geometric shape of a flexible cable suspended from two fixed points.
Week 12
Thanksgiving recess
Week 13
Conservation theorems revisited: conservation of energy, conservation of linearmomentum, conservation of angular momentum. Required reading: Chapter 7, paragraph 7.9. Euler-Lagrange equations with multipliers: forces of constraints. Required reading: Paragraph 7.5. Example problems 7.9, 7.10. See also Lecture notes. The Hamiltonian: Canonical equations of motion – Hamiltonian dynamics. Required reading: Chapter 7, paragraphs 7.10 through 7.11. Example problems: 7.11, 7.12. Energy conservation and conservation theorems in Hamiltonian formulation; The phase space (Paragraph 7.12). See Lecture notes (pages 1-6).
Honors section: Lagrangian mechanics and a family of parametric equations: Lissajous curves; Nonlinear perturbative corrections in Lagrangian mechanics
Homework assignment 9 (Due Dec 7)
HW9 Solutions
Week 14
Poisson brackets and their properties. See Lecture notes (pages 7-10). Fundamental poisson brackets. See notes. Perturbation theory. Perturbative solution of nonlinear (anharmonic) equations of motion. Phase diagrams of nonlinear systems. Self-limiting equations/systems. Chaos. See notes.
Honors section: Problems in Lagrangian and Hamiltonian mechanics.
Week 15
Practice final: Problems, Solutions
Honors section: Problems in Lagrangian and Hamiltonian mechanics.