1. Variational Principles

Question 1

What do variational principles allow us to do?

Answer 1

Extremise quantities e.g. path lengths

Question 2

What is the key result of the Feynman and the swimmer experiment?

Answer 2

Shortest path does not necessarily equal quickest path

Question 3

State Fermat’s principle

Answer 3

Light extremises the optical path

Question 4

See page 1 of document for Snell’s law derivation using Fermat’s princple

Answer 4

Do it lol

Question 5

What is the action used for?

Answer 5

To find the path taken when extremised

Question 6

See page 1 of document for a mathematical representation of the action and the Lagrangian

Answer 6

Do it lmao

Question 7

State Hamilton’s principle

Answer 7

Of all possible paths a system can take, the actualpath minimises the action

Question 8

Outline the steps needed to minimise the action in a problem

Answer 8

1. Use ℓ = T - V
2. Construct a physical path that satifies the boundary conditions
3. Use x(t) and ẋ (t) to get the Lagrangian and substitute into the action equation
4. Minimise the action