Class Title: Mechanics I

Session: Fall 2016 (09/06/2016 – 12/14/2016)
Days & Times: Tu Th 10:00AM – 11:15AM
Location: Hasbrouck Laboratory room 134

Midterm Exam: Thursday 10/13, 10:00AM – 11:15AM at HAS 134
Midterm Exam2: Thursday 11/29, 10:00AM – 11:15AM at HAS 134
Final Exam: Thursday 12/22, 10:30AM – 12:30PM at HAS 134

Additional Honors 421 class (everybody is welcome to enroll!)
Days & Times: Fr 5:30PM – 6:20PM
Location: Hasbrouck Laboratory room 134

Instructor: Tigran Sedrakyan
E-mail: tsedrakyan@physics.umass.edu
Office: HAS 105
Phone:  413-545-2409
Office hours: W 5-8pm. We can meet also after the lectures or other times by appointment.

TA: Nuoya Zhou
E-mail: nuoyazhou@umass.edu
Office: HAS 112
Office hours: Th 3:00PM – 5:00PM

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%

—  Midterm exam ( Thursday 10/13, 10:00AM – 11:15AM at HAS 134, during the regular lecture hour) — 20%.

—  Final exam — 40%.

(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 15)

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 22)

HW2 Solutions (also see Nuoya’s alternative solution to Prob 1 part 3 here)

Honors section: Honors Lecture 1 notes

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.

No Homework is due Sept 29.

Honors section: Honors Lecture 2 notes

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.

Homework assignment 3 (Due Oct 6)

HW3 Solutions

Honors section: Honors Lecture 3 notes

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.

Practice Midterm:  problems; solutions.

Homework assignment 4 (Due Oct 13) — Now due Tue, Oct 18.

HW4 Solutions

Honors section: Required reading: Chapter 4: Nonlinear Oscillations and Chaos, paragraphs 4.1 through 4.3. Example problem 4.1.

Week 6
No lecture on Tue, Oct 11 (because of the Columbus day holiday).
Mid-term exam on Thu, Oct 13.
Midterm: problems; solutions

Honors section: Honors Lecture 5 notes
Required reading: Chapter 4, paragraphs 4.3 through 4.6.

Homework assignment 5 (Due Oct 20)

HW5 Solutions

Week 7
Central-force motion. Required reading: Chapter 8 paragraphs 8.1 through 8.7.  Suggested reading: Chapter 3 paragraphs 14,15 of Landau Lifshitz. See also Lecture 10 notes.
Closed orbits, small perturbations around circular orbits. Marion paragraphs 8.8, 8.9 (optional), 8.10. Example problems 8.5 through 8.7.

Homework assignment 6 (Due Oct 27)

HW6 Solutions

Week 8
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.  Require reading: Chapter 9, paragraphs 9.1, through 9.8. Example problems 9.1 through 9.10.   Dynamics of rigid bodies. Required reading: Chapter 11, paragraphs 11.1, 11.2, example problems 11.1, 11.2.

Homework assignment 7 (Due Nov 3)

HW7 Solutions

Honors section: problem/solution

Week 9
Curves in higher dimensions,  Functionals. Calculus of variations: Euler-Lagrange equation, 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.

Homework assignment 8 (Due Nov 10)

HW8 Solutions

Week 10
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 16 notes.

Homework assignment 9 (Due Nov 17)

HW9 Solutions

Week 11 
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 17 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.

Practice Midterm: problem&solution

Solution to Problem 7-20 (Marion page 283).

Homework assignment 10 (Due Dec 1)

HW10 Solutions

Week 12 
Thanksgiving recess

Week 13
Mid-term exam on Tu, Nov 29: Problems; Solutions
Practice Final: Problems and Solutions

Week 14
Energy conservation and conservation theorems in Hamiltonian formulation; The phase space (Paragraph 7.12); Poisson Brackets and their properties, constants of motion. See Lecture 19 notes.

Homework assignment 11 (Due Dec 13)

HW11 Solutions