Physics 311 Classical Mechanics Welcome! Syllabus. Discussion of Classical Mechanics. Topics to be Covered. The Role of Classical Mechanics in Physics.

Topics Newton’s laws General discussion of differential equations. Energy, work, and potential energy. Time from the energy equation. “Falling Balls” -- velocity-dependent forces: Fluid resistance and terminal velocity. Numerical Methods. Vector analysis Coordinate systems Vector derivatives. More on work and potential energy. Symmetry and conservation laws in classical mechanics. Oscillators The simple harmonic oscillator (SHO). The damped harmonic oscillator. Phase Space. Forced harmonic oscillator. Non-sinusoidal driving forces: Fourier expansions. Non-linear oscillators: methods of solution Examples: Pendula, Duffing’s eqn., Van Der Pol’s osc. Test 1

Topics, continued Motion in 3-D Potential energy and projectile motion in 3-D. The harmonic oscillator in 2-D and 3-D. Charged particles in magnetic and electric fields. Lagrangians The Lagrangian.and Hamilton’s Principle Euler-Lagrange equations Hamilton’s equations and reduction of order. (Special topic) Liouville theorem. (Special topic) Poisson Brackets. Rotating Frames of Reference Accelerated coordinate systems and inertial forces. Rotating reference frames. Dynamics of a particle in a rotating frame of reference. Effects of Earth’s Rotation Foucault Pendulum.

Topics, continued Gravity Central forces Kepler’s Laws. Orbits. Scattering. Systems of particles Center of mass. Energy, momentum, and linear momentum. The reduced mass and the two body problem. The restricted three body problem Hand out take home exam

Topics, continued Systems of particles (continued) Collisions Rocket motion Mechanics of Rigid Bodies Center of mass of a rigid body, and rotation of a rigid body about a fixed axis. Calculation of the moment of inertia. The physical pendulum A general theorem concerning angular momentum Laminar motion. Impulse and collision involving rigid bodies. Rotation of rigid bodies about an arbitrary axis. Principal axes of a rigid body, and Euler’s equations of motion of a rigid body.

The Typical Structure of Physical Theories Force DescriptionsMechanics Electricity & Magnetism Gravity Etc. Classical Mechanics Quantum Mechanics Quantum Field Theory Mechanics tells us how an object will move given a force. We call this the kinematics of the system. Newton’s second law, F = ma is an example of a kinematic equation. It relates the acceleration of an object to the force. We call the description of the forces themselves the dynamics of the system. Gauss’s Law is an example of a dynamical equation.

Classical Mechanics Quantum Mechanics Special Relativity Quantum Field Theory (Newton: ) (Bohr, Heisenberg, Schrodinger, et al.) (Einstein was a big year.) (Dirac, Pauli, Feynman, Schwinger, et al.) The Four Forces to Which Mechanics is Applied: 1.Strong 2.Electromagnetic 3.Weak 4.Gravitational