Course Title: Mechanics
Academic
Year: 1999/2000
Instructor: Birger Bergersen
Credits: 3.0
Term: 2
Lecture
hrs/week: 3
Tutorial
hrs/week: 1
Lab hrs/week: 0
Prerequisites: MATH 217 (or MATH
200, or MATH 226), at least 68% in one of PHYS 122 and PHYS 102, or PHYS 216. Co
requisites: MATH 223 (or MATH 221) and MATH 215.
Required
Text:
No required text. Lecture
notes posted on web.
Course Outline (by week)
Newtonian Mechanics
1. Vector algebra. Newton's laws. Momentum, work and kinetic energy.
Friction.
2. Drag. Dimensional analysis.
Force fields in 2 and 3 D. Stokes theorem.
Lagrangian mechanics
3. Generalized coordinates. Lagrangian equations of motion.
4. Calculus of variations. Examples of calculus of variations
problems.
5. Hamilton's principle. Conservation of energy. The pendulum.
Elliptic integrals. Trajectories in phase plane.
Non-inertial frames of reference.
6. Rotating the coordinate system. Euler angles. Velocity and
acceleration in different coordinate systems. Non-inertial frames of reference.
Midterm
Central forces.
7. Angular momentum. Kepler’s laws.
Properties of the orbits.
Rigid body motion
8. Kinetic energy of a rigid body. Moment of inertia tensor.
9. Lagrangian of a rigid body. Angular momenta and torques. Euler's
equations for a rigid body.
10. Equation of motion for Euler angles. Heavy symmetric top with one
point fixed. Effective potential.
Hamiltonian Mechanics
11. Hamiltonian equations of motion. Poisson Brackets.
12. Canonical transformation. Nonholonomic constraints. Dissipative
forces.
13. Review.
Mark Distribution
Assignments 30 %
Midterm 20 %
Final 50 %
If the mark on the final
is higher than the mark on the regular assignments or the midterm, the final
will be given increased weight. Students have the option of engaging in project
at end of term. If they do the weight given to Assignments, midterm and final
is reduced and the project may contribute up to 15 % of grade.