Intermediate Classical Mechanics

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.