3. Introducing the Hamiltonian

Question 1

What type of time dependence does the Hamiltonian have if ℓ(x, ẋ, t) ?

Answer 1

Explicit time dependence

Question 2

What type of time dependence does the Hamiltonian have if ℓ(x, ẋ) ?

Answer 2

Implicit time dependence

Question 3

Is H conserved?

Answer 3

Yes

Question 4

See page 3 of document for the hamiltonian equation and how the Hamilton = total energy, and how energy is conserved

Answer 4

Do it

Question 5

Describe why the Hamiltonian is easier to use than the E-L equation at times

Answer 5

E-L equation has second order derivatives, whereas the Hamiltonian only has first order