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Physics
507. Classical
Mechanics
(Fall 2011)
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Room: ARC-207
Monday, Thursday;
10:20-11:40 am
Instructor: Sergei
Lukyanov
office: Serin E364
office phone: (732)-445-5500 ext. 4622
e-mail:
sergei@physics.rutgers.edu (the best way)
Office hours: Thursday
4:00-6:00 pm
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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 =
20% Homework +
30% Midterm
+ 50% Final).
Exams: There will be
a midterm (end of October)
and final exams.
Students with Disabilities:
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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://disabilityservices.rutgers.edu/ |
Download this
info in PDF format
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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.
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NEWTONIAN MECHANICS
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- 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)
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Download
syllabus
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Assigned
on
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Assignment
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Due
Date
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1. |
Sep 1,
2011 |
pdf
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Sep 12,
2011 |
pdf
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2. |
Sep 12,
2011 |
pdf
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Sep 19, 2011 |
pdf
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3. |
Sep 19,
2011 |
pdf
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Sep 26,
2011 |
pdf
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4. |
Sep 26,
2011 |
pdf
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Oct
3, 2011 |
pdf
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5. |
Oct 3,
2011 |
pdf |
Oct 10,
2011 |
pdf
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6. |
Oct 10,
2011 |
pdf
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Oct 17,
2011 |
pdf
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7. |
Oct 17,
2011 |
pdf
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Oct 27,
2011 |
pdf |
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Midterm exam:
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Oct 31,
2011
Download program
and ground rules
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pdf
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pdf
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8. |
Oct 27,
2011 |
pdf
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Nov 10,
2011 |
pdf
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9. |
Nov 10,
2011 |
pdf
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Nov 17,
2011 |
pdf
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10. |
Nov 17,
2011 |
pdf
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Dec 1,
2011 |
pdf
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11. |
Dec 1,
2011 |
pdf
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Dec 12,
2011 |
pdf
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Final exam:
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Wednesday,
Dec 21,
2011, 10:00 AM-1:00 PM; Room ARC 108
Download program and ground rules
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pdf
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pdf
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