Recommendation for a book on Hamiltonian Mechanics

[TerryW]

Homework Statement: Practical examples of Hamiltonian Mechanics sought
Relevant Equations: Hamilton Jacobi Equations, MTW

Hi,

I'm currently a bit stuck on Box 24.2 in MTW. I really need to get a better understanding of Hamiltonian Mechanics to be able to work my way through this and I wondered if someone could give me a recommendation for a book on Hamiltonian Mechanics with lots of examples and exercises. If same person could also answer a couple of questions on the actual contents of Box 24.2, that would also be greatly appreciated.

Cheers


TerryW

 

[WWGD]

Hi Terry,
Monday through Wednesday? Not sure everyone knows what MTW stands for. Can you expand?

 

[renormalize]

Monday through Wednesday? Not sure everyone knows what MTW stands for. Can you expand?

I assume MTW = Misner, Thorne & Wheeler Gravitation.

 

[TerryW]

I assume MTW = Misner, Thorne & Wheeler Gravitation.

Correct

 

[TerryW]

42.
It helps if you actually ask the questions.

 

[TerryW]

Well, my main question was seeking suggestions for a good book on Hamiltonian Mechanics and I haven't had any response on that. If anyone had come forward with a suggestion and then maybe offered help with the questions thrown up by Box 24.2, I could then set out my issues with maybe some hope that some help would be forthcoming.

TerryW

 

[haushofer]

I' recommend Tong's online lecture notes on this topic. I used them to better understand Schrödinger's derivation of his equation.

 

[Frabjous]

Greenwood Classical Dynamics.
Are you sure it’s Box 24.2?

 

[TerryW]

I' recommend Tong's online lecture notes on this topic. I used them to better understand Schrödinger's derivation of his equation.

Thanks for the recommendation haushofer.

Cheers

TerryW

 

[TerryW]

Greenwood Classical Dynamics.
Are you sure it’s Box 24.2?

Thanks for your recommendation Frabjous.

You're right, it's Box 25.4 which is causing me the problems, starting with the Hamiltonian for Newtonian Gravity!! Why are the r^2 and (rsin𝜃)^2 in the denominator rather than the numerator?

 

[Frabjous]

They are using generalized momenta, not regular momenta:
$p_i\equiv \frac {\partial L} {\partial {\dot q}_i}$
where $p_i$ is the generalized momenta and L is the lagrangian.

 

[TerryW]

They are using generalized momenta, not regular momenta:
$p_i\equiv \frac {\partial L} {\partial {\dot q}_i}$
where $p_i$ is the generalized momenta and L is the lagrangian.

Thanks for pointing this out. Not immediately obvious but maybe I really do need to do a bit of work on Lagrangian and Hamiltonian mechanics.

Cheers

TerryW

 

[TerryW]

They are using generalized momenta, not regular momenta:
$p_i\equiv \frac {\partial L} {\partial {\dot q}_i}$
where $p_i$ is the generalized momenta and L is the lagrangian.

In the Tong lecture notes recommended by Haushofer there is a line on p21 which really switched a bright light on for me. The line is "... $p_i = \frac{\partial L}{\partial q_i}$ is called the generalised momentum conjugate to $q_i$. (It only coincides with the real momentum in Cartesian coordinates).. Now I get it!

I still have a couple of issues with the content of Box 25.4 - I'll post these shortly.


Regards


TerryW