CLASSICAL MECHANICS
PHY 401
Instructor: Dr. Romulo Ochoa
Office: SC-P132
Phone: 771-3162 e-mail:
ochoa@tcnj.edu
Text: S.T.
Thornton and J.B. Marion, Classical Dynamics of Particles and Systems, 5th
Edition, Thomson/Brooks Cole, 2004
I. Course Description
Newtonian mechanics is studied rigorously using
advanced mathematical and numerical techniques. Topics treated include
kinematics, dynamics, harmonic oscillations, central forces, many particle
systems, rigid bodies, Lagrangians, and Hamiltonians. Scientific programming is used
extensively in problem solving.
II. Course Objectives
1. To develop fundamental concepts in mechanics
more rigorously as needed for further study in physics, engineering and
technology.
2. To apply advanced mathematical and computational
techniques to complex problems.
3. To contribute to the development of the
student’s thinking process through the understanding of the theory and
application of this knowledge to the solution of practical problems.
III. Course Outline
1. Newtonian Mechanics for a Single Particle
(Ch. 2)
Newton's laws
and inertial systems. Simple applications of Newton’s laws, including constant
applied forces, position-dependent forces, time-dependent forces and
velocity-dependent forces, conservation theorems.
Homework 1:
2.3, 2.6, 2.7, 2.9, 2.12, 2.15, 2.23, 2.29, 2.39, 2.52 and additional problems
HW 1
2. Oscillations (Ch. 3)
Linear
restoring force: Harmonic motion. Damped harmonic and forced harmonic motion.
Resonance. Introduction to chaotic motion.
Homework 2: 3.6, 3.10, 3.15, 3.20, 3.40, 3.44 and additional problems HW
2.
Test 1 TBA
3. Lagrangian and Hamiltonian Mechanics (Ch. 6 and 7)
Euler equation and calculus of variations. Hamilton’s variational principle. Generalized coordinates. Lagrange's
equations of motion for conservative systems. Generalized momenta. Ignorable
coordinates. Forces of constraint. Lagrange multipliers. Generalized forces.
Hamilton's equations.
Homework 3: 7.3, 7.4, 7.5, 7.12, 7.14, 7.15, 7.17, 7.22, 7.24, 7.26,
7.28.
4. Gravitation and Central Forces (Ch. 5 and 8)
Gravitational
force between a uniform sphere and a particle. Potential energy in a
gravitational field. Kepler’s laws of planetary
motion. Energy equation of an orbit in a central field. Orbital energies in an
inverse-square field. Effective potential. Orbital transfers: gravitational
boost and braking.
Homework 4: 5.4, 5.7, 5.15, 8.5, 8.10, 8.14, 8.25, 8.28 and additional
problems HW 4
Test 2 TBA
5. Dynamics of
System of Particles (
Center of mass
and linear momentum of a system. Angular momentum and kinetic energy of a
system. Motion of two interacting bodies. Collisions and scattering. Motion of
a body with variable mass: rocket motion.
Homework 5:
9.4, 9.6, 9.10, 9.12, 9.21, 9.23, 9.30, 9.37, 9.42, 9.54, and 9.60.
6. Noninertial Reference Systems (Ch. 10)
Accelerated
coordinate systems and inertial forces. Rotating coordinate systems. Dynamics
of a particle in a rotating coordinate system. Effects of Earth’s rotation. The
Foucault pendulum.
Homework 6:
10.3, 10.6, 10.9, 10.18, 10.20, and 10.22.
7. Mechanics of
Rigid Bodies (
Center of mass
of a rigid body. Rotation about a fixed axis.
Calculation of moment of inertia. Angular momentum. The physical
pendulum. Laminar motion of a rigid body. Center of percussion. Eulerian angles.
Homework 7: additional problems HW 7
Final Exam
IV. Assessment of Student Performance
1. Tests (35
points)
2. Final exam
(35 points)
3. Homework
problems (20 points)
Homework
problems are due one week after the corresponding chapter has been completed in
the lectures unless otherwise noted. Late homework will not be accepted.
Homework should be handed in an ordered and neat presentation; points will be
deducted for lack of these.
4.
Computer program (10 points)
The computer
program is due three weeks after it is assigned.
V. Attendance
Students are
expected to attend class. No makeups will be given unless there is an emergency
situation. In that case students are expected to contact the instructor no
later than 24 hours after the test or exam; otherwise they will be given a zero
grade for the missed evaluation.
VI.
Bibliography
Arya, A. P., “Introduction to Classical Mechanics,” 2nd Ed.,
Prentice Hall, 1998.
Walker, J. “Halliday and Resnick
Fundamentals of Physics,” 8th Ed., J. Wiley & Sons, 2007.
Taylor, J. R., “Classical Mechanics,” University
Science Books, 2005.
Serway, R. A.,
“Physics for Scientists and Engineers,” 7th Ed.,
Thomson-Brooks/Cole, 2008.
Spiegel, M. R.,”Theoretical Mechanics,” Schaum's Outline Series, McGraw Hill, 1992.
Young, H. D. and Freedman, “University Physics,” 11th Ed.,
Pearson/Addison-Wesley, 2004.
VII. Selected TCNJ Policies
Final Examinations
The final exam
is not scheduled until the middle of the semester. Therefore do not
plan on any travel until after the last day of the exam
period. TCNJ’s final examination policy is available on the web:
Attendance
Every student
is expected to participate in each of his/her courses through regular
attendance at all class sessions. It is further expected that every student
will be present, on time, and prepared to participate when scheduled class
sessions begin. While attendance itself is not used as a criterion
for academic evaluations, grading in this course is based on participation in
quizzes to be given at the beginning of several classes. No make-ups or extensions will be given unless a student has a genuine
emergency. If a student misses an exam or assignment deadline they must contact
the instructor within 36 hours to explain the situation; otherwise the student
will earn a zero for that exam or assignment.
Students who
must miss classes due to participation in a field trip, athletic event, or
other official college function or for a religious holiday should arrange with
their instructors for such class absences well in advance. In every instance,
however, the student has the responsibility to initiate arrangements for make-up
work.
TCNJ’s full
attendance policy is available at:
http://policies.tcnj.edu/policies/digest.php?docId=9134
Academic Integrity Policy
Academic dishonesty is any attempt by the student
to gain academic advantage through dishonest means, to submit, as his or her
own, work which has not been done by him/her or to give improper aid to another
student in the completion of an assignment. Such dishonesty would include, but
is not limited to: submitting as his/her own a project, paper, problem set,
report, test, or speech copied from, partially copied, or paraphrased from the
work of another (whether the source is printed, under copyright, or in
manuscript form). Credit must be given for words quoted or paraphrased. The
rules apply to any academic dishonesty, whether the work is graded or ungraded,
group or individual, written or oral.
TCNJ’s academic integrity policy is
available at:
http://policies.tcnj.edu/policies/viewPolicy.php?docId=7642
Americans
with Disabilities Act (ADA) Policy
Any student who has a documented disability and is in need of academic
accommodations should notify the professor of this course and contact the
Office of Differing Abilities Services (609-771-2571). Accommodations are
individualized and in accordance with Section 504 of the Rehabilitation Act of
1973 and the Americans with Disabilities Act of 1992.
TCNJ’s Americans with Disabilities Act (ADA) policy
is available
at: http://affirm.pages.tcnj.edu/key-documents