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## QuantumSycat said

Hi I wondered if i can ask you for some help on something physics related…? its just that i need to find equations of motion from a lagrangian but the lagrangian is complicated….with a determinant and F_{\mu\nu}…..if you can help…i’ll email you my question!

Sy

## peeterjoot said

Go ahead and ask. Is it the field Lagrangian for Maxwell’s equations? That’s the only Lagrangian that I know of the form you describe:

## NN said

Peeter,

Hi. Found your blog randomly and am enjoying going through old posts on things like QM and geometric algebra (finally another soul who thinks its useful).

I have a physics/math problem that I am trying to solve and unfortunately am not at my best in the math part of it. I am hoping that you might be able and willing to help me.

I want to solve a coupled set of 2nd degree differential equations from arbitrary initial conditions (it is the non-steady state behaviour which most interests me). Numerical approximate solution is fine – but I haven’t been able to find a suitable free solver (I no longer have access to things like Mathematica).

the equations (with constants removed) are: (ddt = second time derivative)

ddt[x1] = -x1 + (sin[x2]-x1)

ddt[x2] = -(sin[x2]-x1)*cos[x2]

Sorry, I can’t really format it more effectively in text.

*Bonus points if you can figure out why I want to solve it….

## peeterjoot said

For , you can Taylor series expand the RHS around some point . That leaves you with an equation of the form

. If is diagonalizable you have a solution in the nieghbourhood of this point:

. I don’t know how numerically stable such an approach is, and the compuational complexity probably sucks. There’s probably much better ways, but that’s the way that seems obvious to me.

Looks like I don’t win your bonus points.

## peeterjoot said

two related posts of mine on just this:

https://peeterjoot.wordpress.com/2009/11/18/linearizing-a-set-of-regular-differential-equations/

https://peeterjoot.wordpress.com/2009/10/11/hamiltonian-treatment-of-rigid-spherical-pendulum/

## NN said

Could theoretically work… I really like the linearization trick. Unfortunately I suspect that this type of expansion would blow up for the specific behaviour that I am interested in and rapidly degenerate into unphysicality.

Of course, there may well be other ways of couching the problem to begin with that I am missing. Would you be willing to let me send you a short description (where I can insert a figure and a few equations) and see if I can get you interested?

## peeterjoot said

You can send it, but I can’t promise to be interested;) What’s the origin of your problem (ie: the bonus question)?

## NN said

Yes… send it… I don’t know an email to send it to… (Though your blog has mine)

## Syungb said

Hello Peeter,

I am one of your classmates at PHY356(I talked with you after the last lecture).

I just took one of my finals, and now it’s time for me to study QM & EM. This semester (whoever in 3rd year as full-time) is the hardest, I think..considering how much study and how many assignments we have to do at the same time.

Thank you for your beautifully organized blog!! and for you too of course!

I hope you are having a great day!

## peeterjoot said

I’m glad if any of my notes help somebody else other than myself too. Did you find the practice exams. There’s only one that I find for PHY356H, but there’s also two older ones under 355:

http://exams.library.utoronto.ca.myaccess.library.utoronto.ca/simple-search?query=PHY355H

I’ve done the questions from one of the old exams now, and it took me much longer than 3 hrs. This may be a tough test!

## Voices said

Hi peter, just seen your beautiful blog. I found this looking for solutions to a problem particularly the one below. It is to find the point of intersection of the two curves by Newtons method..

0.3, t≤5

d(t)= { {1+sin(π(t-8)/16)}, 519

0, t≤5

s(t)= { 2.5 sin〖(π(t-4)/16),〗 5<t≤18 ……….. (2)

0, t≥18

I have the idea we have to start from g(t)=d(t)-s(t). But getting stuck from going further….

## peeterjoot said

I explored newton’s method for intersection of curves in the following post:

https://peeterjoot.wordpress.com/2010/03/07/newtons-method-for-intersection-of-curves-in-a-plane/

(see the intersection of curves part at the end). Remember that newton’s method is essentially following the slope to the intersection. You want to setup your problem that way.

## Voices said

I could not proceed. I have already gone through tht one prior to writing you. are we using the general method with the formula x_(n+1)=x_n-(f(x_n))/(f^’ (x_n))….?? But to which equation are we using this formula? I could not find the equation g(t)=d(t)-s(t) from the two equations given above.

## Voices said

how to find a single equation from the two above-g(t)=d(t)-s(t)? are we using the formula for the x values using

x_(n+1)=x_n-(f(x_n))/(f^’ (x_n))…? I could really not find the single eqation for this from the two.

## peeterjoot said

I suggest you go back and review the geometry of how Newton’s method works before you tackle two curves. The form that you indicate is following the slope of the curve down to the horizontal axis from one curve. This also works for two curves, but you have to find the tangent to each of the curves at the point you pick for your first iteration and follow those tangents to their intercepts. Then repeat. If I calculated this right, the iterative formula is given by (4.20) in the link that I provided, but I’d highly encourage you to attempt that yourself

## Verbeia said

Dear Peeter,

I noticed you were one of the people who committed to the previous Mathematica proposal on StackExchange. Unfortunately, it was closed by StackExchange management for what many people thought were misguided reasons.

http://discuss.area51.stackexchange.com/questions/3738/mathematica-proposal-has-disappeared

The solution advocated by the same management, was to re-create the proposal and ramp support a bit more this time. This is what we have done.

http://area51.stackexchange.com/proposals/37304/mathematica

Please re-join if you are still interested

## peeterjoot said

I’ve re-followed, but don’t see a way to commit.

## Jonas said

Dear Peeter,

I found you having had a problem with Lyx and the ClassicThesis template at http://www.latextemplates.com/template/masters-doctoral-thesis. As I am having the same problem right now, I wonder if you could find a solution.

Thanks

Jonas

## Aniket said

I am a Physics undergrad, and I find your blog very useful. I wonder how you get time to do so much stuff. Though, I am a full time student, it is still difficult to get time, to study it yourself, and write about it in such detail. How do you manage time?

## peeterjoot said

Some of this is a product of taking courses … I take the lecture notes live in class in latex and usually have a mostly finished pdf by the time the class is done (I’m a fast typer;) I also usually handdraw figures because generating them nicely is usually time intensive (much more so than any latex).

That doesn’t mean that it doesn’t take time … I do tend to at least attempt to go over my notes after the lecture to fill in the bits I didn’t understand. If a lot was glossed over in class, this post processing can take a fair chunk out of the time I have to allocate to study and problems.

This year time demands have been particularly taxing, and I haven’t been able to post my notes (advanced classical optics) in the old fashion to wordpress one at a time, instead have been accumating them and posting directly as pdf to https://sites.google.com/site/peeterjoot2/ (only once so far, around the midterm).

I think that you’ll find that no matter how you schedule your time it will always be a challenge to find enough. You have that trouble as a full time student (plus possible part time work ?, and any extra-curricular activities). I have that trouble working part time (80% hours), being a dad, taking my one course per session, doing stuff around the house, and learning a bit of martial arts. I’m pretty stretched for time, and certainly don’t have enough. If you can tell me how to get some I’d appreciate it;)

Peeter

## Leonard said

Hi Peeter, I found your blog while looking for an answer to one of the Mechanics (Landau) problems. Given that physics is your hobby, and so is mine, could you give me a hand with the problem 2 (c) of $11 in Mechanics by Landau. The problem is to find the period for a given potential. It’s just a matter of integrating… but after 3 hours I don’t know how to solve it.

Thanks

## Anon said

Hey Peeter, I found your blog while working on problem sets for PHY452. I just wanted to ask you if prof. Paramekanti said what the average was for the first midterm. Do you also think there might be some minor bell curving? I’m hoping, so that I may reach an 80 in the course:P

Thanks

Anon

## peeterjoot said

He did say what it was, but I don’t recall exactly (it was very low, 8/15 or so I think). The average on the second midterm was also low, but not as bad. I seem to recall 9.03/15 for that one.

## Anon said

Do you he’ll bell curve?

## peeterjoot said

He did say he was going to adjust the scores in some fashion, but didn’t specify details.

## Anon said

Oh okay, thanks!