PHYS 351 - Fall 2021

Classical Mechanics

What does "Classical" mean?

How much do we know?

Where is this ball located right now? Be precise as possible.

What is its velocity? Be precise as possible.

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."

Pierre Simon, Marquis de Laplace. (~1814)

A particle is moving in the x-direction and is confined between two perfectly bouncy (ahem, elastic) walls so that it bounces back and forth between $x=0$ and $x=l$, where $l$ is the distance between the two walls. If there is an uncertainty in the initial velocity measurement, i.e. $\Delta v_0$, find the subsequent uncertainty in position at time $t$ later.

Let a particle start from point A and move towards B. Assuming this is a perfect circle and that collisions with the walls are totally elastic, will it ever come back to point A? If so, how many bounces will it take?

A particle bounces off the inner walls of a circular constraint.

Time

If we know how things move in the forward direction of time, can we also know how the process would happen in reverse?

The Outline

  1. Newtonian Mechanics
  2. Special Relativity
  3. Variational Principle
  4. Lagrangian & Hamiltonian Mechanics
  5. Gravitation
  6. Accelerating Reference Frames
  7. Rigid Body Dynamics
  8. Coupled Oscillators
  9. ...and ?

Tools

  • Everything from 20700 and 20800
  • Advanced Calculus and other Math
  • Computers

Intro Physics Review

Largely Mechanics (i.e. 20700) but with some references to electric fields and other 20800 material.

What are Newton's 3 Laws of motion?

What are the implications of the conservation of Energy?

... and Momentum?

... and Angular Momentum?

What goes on the R.H.S.?

$$ \frac{dU}{dx} = \rm{?}$$

Math you'll need

Differential Equations
$$\frac{dv}{dt} = \frac{F}{m}$$

But what if $F$ is messy?

Taylor Series
Vectors

To open the door, which direction should the torque vector point?

Linear Algebra

Computational Physics

Quick, you have 5 minutes to prepare a plot of: $$U(x) = -\frac{1}{x}e^{-x}+\frac{1}{5x^2}$$ What do you do?