UBC logo
 
  PHYS 306, Jan-April 2014

PHYS 306 - 201 , Advanced Dynamics


Instructors

Prof Brett Gladman
Tel: (604) 822-6244
Room 330A, Hennings (Physics and Astronomy) Building

Dr Mayra Tovar
Tel: (604) 822-5527
Room 334, Hennings (Physics and Astronomy) Building


Office Hours

Mirko Moeller, Henn 271, moellerm@phas.ubc.ca
No open office hours remain; contact if you wish

Emmanuel Fonseca, Henn 310, efonseca@phas.ubc.ca
No open office hours remain; contact if you wish

Professor Gladman, Henn 300B

Tuesday April 8, 13:00-14:00
Wednesday April 9, 13:00-14:00
Thursday April 10, 14:00-15:00
Friday April 11: 11:00-12:00

Homework

Click on this link to access Homework 6 (PDF file). Homework 6 Solutions (PDF file). See Emmanuel if you have questions.
due Monday April 7, 5PM, in the PHYS 306 box just outside the entrance to Henn 310. You may NOT submit this by email.

OLD HOMEWORKS

Click on this link to access Homework 5 (PDF file) Homework 5 Solutions (PDF file). See Mirko if you have questions.

Click on this link to access Homework 4 (PDF file). Homework 4 Solutions (PDF file). See Emmanuel for questions.

Click on this link to access Homework 3 (PDF file). Homework 3, problem 1 solutions (PDF file) Homework 3, problem 2+3 solutions (PDF file)

Click on this link to access Homework 2 (PDF file). Homework 2 Solutions (PDF file)

Homework 1 Solutions (PDF file, HW1 page on old web site, below)


COURSE INFORMATION

Older info at Old P306 web site

WHEN: January - April 2014.

LECTURE LOCATION: MWF 13:00 - 13:50 in Hennings 202.

TUTORIAL: Each student attends one tutorial a week. Tutorials provide supporting material and problem practice. They are not optional.
March17tutorial (PDF file) and solutions (PDF file)

AIM: Bring students to an advanced undergraduate level in classical mechanics (at the level of Hamiltonian mechanics).

LEVEL: Third-year undergraduate

TEXTBOOK: Mechanics, by Landau and Lifshitz

Grading scheme: Homeworks: 25%, Midterm 25%, Final exam 50%

MIDTERM EXAM: Friday March 14, in class 13:00-13:50

        The 2014 Midterm (PDF file). Midterm Solutions (PDF file)

FINAL EXAM: Monday April 14, 8:30-11:00, IBLC 182 (Barber Learning Centre)
        The final exam will not provide a formula sheet, nor will any calculators be allowed.
        Formulae will be provided except for the 'Memorizable' list provided at the bottom of this web page.


Course Topics

List of topics covered in PHYS 306 lectures

Newton's laws
- conservation of linear and angular momentum
- center of mass

Rigid bodies (The rigid body unit is not covered in the 2014 final exam)
- velocity in space
- Kinetic energy, the Inertia tensor
- Moments of inertia
- Angular momentum of a rigid body
- Principle axes
- Euler Angles
- Free precession, Euler's equations, example of Chandler wobble
- Symmetric top as an example of forced precession

Lagrangian mechanics
- degrees of freedom
- generalized coordinates
- the action
- Hamilton's principle, or principle of least action
- Generalized forces
- Euler-Lagrange equations
- Getting eqs of motion via newtonian and lagrangian methods
- concept of cyclic coordinates = conserved quantities/symmetries

General Mechanics
- Energy
- turning points
- The 'simple' rigid-rod pendulum
- Damped oscillators
- Forced oscillators (resonance)
- Projectile motion, without and with air resistance
- velocity and acceleration in non-inertial reference frames
- Central force problems: 
  - effective potential
  - the equation of orbit 
  - conic sections
  - the motion in time, Kepler's equation
  - Rutherford scattering

Hamiltonians and Hamilton's equations
  - Legendre transformation
  - construction of Hamiltonians
  - structure of Hamilton's equations and phase space
  - Canonical transformations
  - Constants and integrals of the motion
  - Poisson brackets
  - the Hamilton-Jacobi equation, and method

---- Following topics of last lecture not examinable ----
- Transition to quantum mechanics 
- Determinism, Dynamical chaos
- Lyapunov exponents

Memorizable Physics equations (not just for this course; forever!):

- Principle of least action
- Euler-Lagrange equations
- kinetic energy for free particle in cartesian coords (in v's and p's)
- Potential function for S.H.O. and kepler problem in cartesian
- defintion of generalized momenta (as partial of Lagrangian)
- Hamilton's equations
- Names given to accelerations/forces in rotating reference frames
- 2nd order eqs of motion of the 1-D S.H.O. and simple pendulum.
- Kinematics equations (from high-school!) for 1-D constant acceleration
- circular motion in a radius r requires a central acceleration of v^2/r