Advanced Mechanics I

PHYS 6412, Fall 2018


Instructor:        Prof. Julian Velev

Office:               Natural Sciences II, C-346



Class period:    Tuesday and Thursday, 11:30-12:50, room C-311

Office hours:   Tuesday and Thursday, 13:00-14:00 or by appointment


Course description: This course will reiterate the subject of classical mechanics familiar to the student from undergraduate courses. However, this will be done on firm ideological and mathematical grounds. This will give the student the opportunity to learn a number of important mathematical techniques which are used in other branches of physics and in other fields. In addition, the advanced formulation of classical mechanics is a stepping stone to various other branches of modern physics such as quantum mechanics, statistical mechanics, etc. The course will cover the Lagrangian and Hamiltonian formulation of mechanics; conservation laws; and integration of the equations of motion for the one and two body problems. Important special cases will be covered in detail, such as motion in a central field; motion of a rigid body; and small oscillations.


Prerequisites: The students should be familiar with the Newtonian formulation of mechanics (undergraduate courses) and should have sufficient mathematical proficiency.


Textbooks: (1) L.D. Landau and E.M. Lifshitz, Mechanics (Vol. 1, Third Edition), Elsevier, ISBN 0750628960; (2) H. Goldstein, Classical Mechanics (3rd Edition), Addison-Wesley, ISBN 0201657023


Grading: There will be three exams, each exam counts for 30% of the grade. The exams will be in class and non-cumulative. The remaining 10% of the grade will be for class attendance and participation, and for doing reading and homework assignments.


Special provisions: (1) Missed classes: if a class is lost due to travel or other circumstances I will assign times when the class will be made-up and/or assign equivalent reading and homework assignments; (2) Special arrangements: homework extensions, make-up exams, and other exceptions can be granted given sufficient reason and advanced notice.


Academic integrity: The University of Puerto Rico promotes the highest standards of academic and scientific integrity. Article 6.2 of the UPR Students General Bylaws (Board of Trustees Certification 13, 2009-2010) states that academic dishonesty includes, but is not limited to: fraudulent actions; obtaining grades or academic degrees by false or fraudulent simulations; copying the whole or part of the academic work of another person; plagiarizing totally or partially the work of another person; copying all or part of another person answers to the questions of an oral or written exam by taking or getting someone else to take the exam on his/her behalf; as well as enabling and facilitating another person to perform the aforementioned behavior. Any of these behaviors will be subject to disciplinary action in accordance with the disciplinary procedure laid down in the UPR Students General Bylaws.


Tentative class schedule:






Survey of Newtonian mechanics

G 1.1-2

Aug. 21-23




Principle of least action. Calculus of variations

L 1-2

Aug. 28-30



G 1.3; 2.1-5


Lagrangian formalism

L 3-5

Sep. 4-6



G 1.4-6



Conservation laws

L 6-10

Sep. 11-13



G 2.6-7; 3.4


Integration of the equations of motion in 1D

L 11-12

Sep. 18-20






Ch. L 1-3; G 1-3

Oct. 2


Motion in a central field

L 13-14

Sep. 25-27



G 3.1-3,5-6


Kepler’s problem

L 15

Oct. 4-9



G 3.7-9


Small oscillations in 1D

L 21-22,25

Oct. 11-16



G 6.1,5


Principal axis of oscillations. Vibration of molecules

L 23-24

Oct. 18-23



G 6.2-4



Ch. L 3,5; G 3,6

Nov. 1


Rigid body motion

L 31-34

Oct. 25-30



G 4.1-3; 5.1-4



Euler angles. Euler's equations

L 35-36

Nov. 6-8



G 4.4,6; 5.5-7



Hamiltonian formalism

L 40-41; 43-44

Nov. 13-15



G 8.1,3,5-6



Conservation laws. Poisson bracket

L 42

Nov. 20-27



G 8.2; 9.5



Canonical transformations

L 45-46

Nov. 29-Dec. 4



G 9.1-4, 7




Ch. L 6,7; G 4,5,8,9

Dec. 6

G – Goldstein; L – Landau & Lifshitz