Physics 311Classical 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 systemsVector 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 PrincipleEuler-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

GravityCentral 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)

CollisionsRocket 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 momentumLaminar 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 Descriptions Mechanics

Electricity & MagnetismGravityEtc.

Classical MechanicsQuantum MechanicsQuantum 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: 1642-1727)

(Bohr, Heisenberg, Schrodinger, et al.)

(Einstein. 1905 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