Intermediate Classical Mechanics
Curriculum guideline
Lecture: 4 hours/week
The classroom time will be used for a mixture of lectures, solutions of selected problems, and/or in-class assignments (which may include work in groups). Work outside of class time may include pre-readings, self-study, and assignments. Some assignments may be conducted online.
- Vectors and curvilinear coordinates
- Newtonian mechanics
- Motion of projectiles and charged particles
- Conservation of momentum and angular momentum
- Work and conservation of energy
- Conservative forces, potentials, and fields
- Simple harmonic motion
- Euler-Lagrange equations
- The Lagrangian and generalized coordinates
- Symmetries and conservation laws
- Couple oscillators and normal modes
- Central forces and gravitation
- Non-inertial reference frames
- Rotational motion of rigid bodies
Upon successful completion of the course, students will be able to:
- apply Newton's laws of motion in inertial and non-inertial reference frames;
- solve problems in two- and three-dimensions using cartesian, polar, cylindrical, and spherical coordinate systems;
- analyze projectile motion with linear and quadratic drag;
- describe and analyze helical motion (for example, the motion of a charged particle in magnetic fields);
- apply conservation of momentum, angular momentum, and energy to solve problems involving systems of objects;
- explain and apply the relationships between potential and potential energy and the associated field and force respectively;
- describe and analyze oscillations arising from simple, driven, and damped harmonic motion, including the case of resonance;
- define the generalized coordinates of a physical system and use these coordinates to derive the Lagrangian of that system;
- apply Lagrange’s equations of motion in place of Newton's equations of motion to solve problems where appropriate;
- identify symmetries in the variables of a Lagrangian, and explain the connection of these symmetries to conservation laws;
- describe the motion of coupled oscillators using normal modes starting with Lagrange’s equations and Newton’s equations;
- analyze and solve two-body central forces problems;
- derive and apply Kepler’s laws and the equations of orbits;
- describe and analyze phenomena in rotating reference frames such as centrifugal forces and Coriolis forces;
- explain the phenomenon of tides and the behavior of a Foucault pendulum;
- determine the moment of inertia for a rigid body rotating about any axis;
- describe and determine the rotational motion of rigid bodies.
Assessment will be carried out in accordance with Douglas College Evaluation Policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on the following:
| Assignments/In-Class Work | 0-40% |
| Tests (minimum of two) | 30-70% |
| Attendance/Participation | 0-10% |
| Final Exam | 30-40% |
| Total | 100% |
Consult the Douglas College Bookstore for the latest required textbooks and materials. Example textbooks and materials may include:
John R. Taylor. (Current Edition). Classical Mechanics. University Science Books.
Morin, David. (Current Edition). Introduction to Classical Mechanics. Cambridge University Press.
Goldstein, Herbert, John Safko, and Charles P. Poole. (Current Edition). Classical Mechanics. Pearson.
Courses listed here must be completed either prior to or simultaneously with this course:
None.