1. Physics 319 Classical Mechanics
G. A. Krafft
Old Dominion University
Jefferson Lab
Lecture 1
G. A. Krafft
Jefferson Lab

2. Mechanical Motion General classes of motion
Translation: movement from one location to another. Example: driving a car
Rotation: “circular” motion of a body around a fixed axis of rotation. Examples: earth’s rotation about the axis through the north and south poles, motion of a spinning top
Oscillation: repetitive motion displayed by some objects. Examples: pendula or driven electrical circuits
Revolution: orbital motion about centers of attraction. Examples: Lunar motion about the earth, planetary motion about the sun, solar system motion about the galaxy, …..

3. Classical or Analytical Mechanics
Set of general methods, fundamentally based on Newton’s laws and mechanics, for finding and solving the differential equations for the motion of bodies.
Requirements for a classical description to be valid:
Velocities much less than the speed of light (non-relativistic), otherwise need relativistic mechanics
Bodies described are macroscopic and large (non-quantum), at atomic and nuclear scales need quantum mechanics
Gravitation fields are weak and constant (Newtonian) and accelerations non-relativistic, more generally will need Einstein’s General Relativity for an adequate description (no black holes in this course!)

4. Formulations of Mechanics
Newtonian
Developed in Principia to synthesize and explain countless observations about celestial bodies. Used to “prove” the law of universal gravitation. Solved the two body gravitational problem in detail, as we shall.
Lagrangian
Method more general than Newton’s method as it yields equations of motion in a general form that can apply in, for example, accelerating frames of reference. We will use this formalism a lot.
Hamiltonian
Most advanced formulation mathematically. A chapter in Taylor we won’t get to. You will in graduate school. Important for formulating quantum mechanics.
See Radyushkin for some history

5. Fundamental Quantities
Positions in space
Measured by lengths (projections on coordinate axes)
Space is a three dimensional Euclidean (vector) space
Continuous “manifold”
Time
Measured by some repeating phenomenon (stopwatch, quartz crystal, atomic clock, ….
In CM does not change for a moving observer
Continuum
Mass
Resistance to acceleration
Fundamentally discreet; if N>>1 approximately continuous

6. Vectors in 3D

7. Vector Properties Vector addition by parallelogram rule
Scalar Multiplication
Length or norm

8. Scalar Vector or Dot Product
Takes two vectors as inputs and yields a number (scalar)
Linear in both inputs and symmetrical
For normal (perpendicular) vectors vanishes
Maximum when vectors parallel (co-linear)
Get the vector norm by

9. Vector Cross Product
Takes two vectors as inputs and yields a normal vector
Linear in both inputs and anti-symmetrical
For co-linear vectors vanishes
Maximum when vectors perpendicular
Norm of the vector product is the area of parallelogram spanned by the input vectors
Important when rotations involved