1
vote
0answers
233 views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= ...
7
votes
2answers
158 views

Does Hamilton Mechanics give a general phase-space conserving flux?

Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltionian theory like the flux of an ideal fluid, which doesn't change ...
0
votes
1answer
340 views

Why is kinetic energy only “often $1/2mv^2$”?

I am reading the first few pages of Nakahara and refreshing my memory on physics I learned a while ago as a physics math undergrad. Nakahara defines a field $F$ to be conservative if it's the gradient ...
0
votes
0answers
52 views

A posteriori solution to the Hamilton Jacobi equation

I was wondering about the following: For many simple systems it is far too cumbersome to solve the Hamilton Jacobi equation compared with the Hamilton or Lagrange formalism. Now I was wondering, ...
2
votes
1answer
342 views

Canonical transformation generated by hamiltonian?

Someone told me that, in a hamiltonian system, the hamilonian function is the generating function of the canonical transformation given by time translation. However, this statement doesn't make any ...
2
votes
1answer
127 views

Hamiltonian of polymer chain

I'm reading up on classical mechanics. In my book there is an example of a simple classical polymer model, which consists of N point particles that are connected by nearest neighbor harmonic ...
3
votes
1answer
265 views

Find the Hamiltonian given $\dot p$ and $\dot q$

I have these equations: $$\dot p=ap+bq,$$ $$\dot q=cp+dq,$$ and I have to find the conditions such as the equations are canonical. Then, I have to find the Hamiltonian $H$. To answer to the first ...
0
votes
2answers
280 views

Hamiltonian and non conservative force

I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $ \vec {A}= B/2 (-y, x, 0)$. I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is ...
3
votes
3answers
804 views

When Hamiltonian and the total energy are the same

In which condition, the Hamiltonian is the same as the total energy of the system, or say $H=T+V$?
3
votes
3answers
851 views

Is there a valid Lagrangian formulation for all classical systems?

Can one use the Lagrangian formalism for all classical systems, i.e. systems with a set of trajectories $\vec{x}_i(t)$ describing paths? On the wikipedia page of Lagrangian mechanics, there is an ...