Physics 507.  Classical Mechanics   (Fall 2015) 

Course info      |     Plan of lectures   |  Homeworks assignments     |     Useful Links      |     E-mail

Course info

Room: ARC-203
           Monday,   Thursday;   12:00-1:20 pm

Instructor: Sergei Lukyanov
         office: Serin E364
         office phone: (848) 445-9060  
         e-mail: sergei@physics.rutgers.edu (the best way)

Office hours: Thursday 4:00-6:00 pm



Text Books: H. Goldstein, Classical Mechanics
                   Addison Wesley, Third edition.         

    or/and    L. D. Landau, E.M.  Lifshitz
                  Mechanics, Butterworth Heinemann, Third edition.

 
Homework: There will be a homework assignment each week.
                   Late homework will not be accepted. Homework will be graded and give an                    important contribution to your final grade (final score = 30% Homework +                                       30% Midterm + 40% Final). 

Exams: There will be a midterm (October 29?) and final exams.

Students with Disabilities:

If you have a disability, it is essential that you speak to the course supervisor early in the semester to make the necessary arrangements to support a successful learning experience. Also, you must arrange for the course supervisor to receive a Letter of Accommodation from the Office of Disability Services. For more information, see http://www.physics.rutgers.edu/ugrad/disabilities.html

Download this info in PDF format

 

Plan of  lectures

This is a tentative schedule of what we will cover in the course. It is subject to change, often without notice. These will occur in response to the speed with which we cover material, individual class interests, and possible changes in the topics covered. Use this plan to read ahead from the text books, so you are better equipped to ask questions in class.
 

 

 

                               NEWTONIAN MECHANICS


  •  NEWTON's  LAWS (Survey of undergraduate level mechanics):  Time. Reference frame. Material point (particle). Velocity. Galilean transformations and principle of relativity). Newton's laws. Mass and force. Examples of forces.
    Literature:
    1) P. Lampert. Course Notes (Chapters 1.1-1.2)
  • 2) P. Lampert. Course Notes (Chapters 7.1-7.3)                                                                                 
  • SYSTEMS  OF PARTICLES (Survey of undergraduate level mechanics): Internal and external forces. Linear and angular  momentum. Energy. Conservativee and nonconservative forces. Virial theorem.   
    Literature: 1) P. Lampert. Course Notes (Chapter 1.1-1.2) 
    2) H. Goldstein: Classical Mechanics (Chapters 1.1, 1.2, 3.4);
    3) L.D. Landau and E.M. Lifshitz: Mechanics (Chapters 8, 10).
                                          
  •  MOTION IN ONE DIMENSION:  Local solution of Newton equation.  Phase curves.
    Literature:
       1)  L.D. Landau and E.M.  Lifshitz: Mechanics (Chapter 11)     
    2) P. Lampert. Course Notes (Chapters 4.1-4.2) 
      
  •  TWO-BODY PROBLEM:  Reduced mass.  Motion in a central field. Second Kepler law. Binet's equation.
    Literature:  1) H. Goldstein: Classical Mechanics (Chapters 3.1-3.5)
    2)  L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 13, 14) 
    3) P. Lampert. Course Notes (Chapter 4.3) 
  •  KEPLER PROBLEM                              
    Closed orbits. The Laplace-Runge-Lenz vector.                                          
    Literature:  1) H. Goldstein: Classical Mechanics (Chapters 3.7-3.9)
    2)  L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 15) 
    3) P. Lampert. Course Notes (Chapter 4.4) 
  •  SCATTERING
    Differential scattering cross section. Rutherford's formula.
    Literature:  1) H. Goldstein: Classical Mechanics (Chapters 3.10-3.11)  
    2)  L.D. Landau and E.M.  Lifshitz: Mechanics, Chapters 18,19

                                                                          

                      LAGRANGIAN MECHANICS         

                                     

  •   CONFIGURATION SPACE  
        Generalized coordinates. Examples (cylindrical, spherical,
        ellipsoidal coordinates). Generalized velocities. Kinetic energy.
        Holonomic constraints. Degrees of freedom.  
       Literature: 1) R.A. Sharipov, Quick Introduction to Tensor Analysis,
       (Chapters III- VI); 
       2) P. Lampert. Course Notes (Chapters 2.1-2.2) 
       3) H. Goldstein: Classical Mechanics (Chapter 1.3)
       4) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapter 1) 
  •                                                                           

                          RIGID   BODY   MOTION         

                                         

  •   KINEMATICS OF RIGID BODY MOTION  
        Configurational space of a rigid body.
        Euler angles. Angular velocity.
        Literature: 1) H. Goldstein: Classical Mechanics (Chapters 4.1-4.8)
        2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 31, 35) 
    • THE LAGRANGIAN FOR A RIGID BODY  
      Inertia tensor. Principal axis. Angular momentum and kinetic energy of a rigid body. Heavy symmetrical top. Rigid body in contact. Non-holonomic constraints.  
      Literature: 1) H. Goldstein: Classical Mechanics (Chapters 1.3, 2.4, 5.1-5.4, 5.7)
      2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 32-34, 38) 
    • THE EQUATION OF MOTION OF A RIGID BODY  
      Euler's equations. Free assymetrical top.  
      Literature: 1) H. Goldstein: Classical Mechanics (Chapters 5.5, 5.6)
      2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 34, 36, 37) 
    • MOTION IN A NON-INERTIAL FRAME OF REFERENCE (self-study)  
      Coriolis force.  
      Literature: 1) H. Goldstein: Classical Mechanics (Chapter 4.10)
      2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapter 39) 
    • 3) P. Lampert. Course Notes (Chapters 7.4-7.6)

                                                                              

                          SMALL   OSCILLATIONS            

                                         

  •   OSCILLATIONS OF SYSTEMS WITH MORE THAN ONE DEGREE OF FREEDOM  
      Formulation of the Problem. Pair of forms. Characteristic frequencies.
      Normal coordinates (modes).
      Literature: 1) H. Goldstein: Classical Mechanics (Chapters 6.1-6.4)
        2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 21, 23, 24)
        3) P. Lampert. Course Notes (Chapters 3.1-3.3 )
        4) P. Lampert. Course Notes (Chapters 5.1-5.7) 
  •                                                                           

                          HAMILTONIAN MECHANICS         

                                         

  •   CANONICAL EQUATIONS  
        Legendre transformation. Phase space. Hamiltonian.
        Canonical equations of motion. Hamiltonian and energy.  
       Literature: 1) H. Goldstein: Classical Mechanics (Chapters 8.1, 8.3)
       2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 40, 41) 
       
  •   VARIATIONAL PRINCIPLE AND LIOUVILLE's THEOREM  
        Modified Hamilton's principle. Liouville's theorem.  
       Literature: 1) H. Goldstein: Classical Mechanics (Chapters 8.6, 9.9)
       2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapter 46) 
       
  •   POISSON BRACKET  
        Poisson bracket. The angular momentum Pooisson bracket  
        relations. Integrals of motions. Liouville-Arnold theorem
        (week form).
       Literature: 1) H. Goldstein: Classical Mechanics (Chapters 9.5-9.7)
        2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapter 42) 
       
  •   CANONICAL TRANSFORMATIONS  
        Canonical transformations. Generating functions.
       Literature: 1) H. Goldstein: Classical Mechanics   
        (Chapters 9.1-9.3)
        2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapter 45) 
       

                                                 

                          HAMILTON-JACOBI   THEORY            

                                         

  •   HAMILTON-JACOBI EQUATION  
        Hamilton-Jacobi equation. Separation of variables.  
       Literature: 1) H. Goldstein: Classical Mechanics
        (Chapters 10.1-10.5)
        2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 47, 48) 

  •   ANGLE-ACTION VARIABLES  
        Angle-action variables. Adiabatic invariants.  
       Literature: 1) H. Goldstein: Classical Mechanics
        (Chapters 10.6-10.8, 12.5)
        2) L.D. Landau and E.M.  Lifshitz: Mechanics (Chapters 49, 50, 52) 

  • Download syllabus

     

    Homeworks   

    The assignments are stored in PDF format. You can view them using Adobe Acroreader or GhostView The absolute cutoff time for homework is 4pm.
     


    Assigned on
    Assignment
    Due Date
     
    1. Sep 3, 2015 pdf   Sep 14, 2015 pdf  
    2. Sep 10, 2015 pdf   Sep 17, 2015 pdf  
    3. Sep 17, 2015 pdf   Sep 24, 2015 pdf 
    4. Sep 24, 2015 pdf   Oct 1, 2015 pdf  
    5. Oct 1, 2015 pdf Oct 8, 2011 pdf 
    6. Oct 8, 2015 pdf  Oct 15, 2015 pdf  
    7. Oct 15, 2015 pdf   Oct 22, 2015 pdf  


    Midterm exam:


    Oct 29, 2015 (?)
               Download program and ground rules


    pdf  
    pdf  
    8. Oct 29, 2015 pdf  Nov 5, 2015 pdf  
    9. Nov 5, 2012 pdf   Nov 12, 2015 pdf  
    10. Nov 12, 2015 pdf  Nov 19, 2015 pdf  
    11. Dec 3, 2015 pdf   Dec 10, 2015 pdf  
     
             


    Final exam:


    Dec 15-22, 2015, 10:00 AM-1:00 PM; Room ARC
                 Download program and ground rules


    pdf  
    pdf  

    Useful Links  
    1. "Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables",
    M. Abramowitz and I. Stegun
    2. R.A. Sharipov, Quick Introduction to Tensor Analysis
    3.  P. Lampert. Course Notes
       
       

    Course info     |     Plan of lectures  |     Homeworks and Solutions     |     Useful Links     |     E-mail