This isn't homework but could be labeled "textbook style" so I'm posting it here.
Homework Statement
I'm trying to solve
\frac{\partial^2 u} {\partial x^2} +\frac{\partial^2 u} {\partial y^2}=0
on the domain x \in [-\infty,\infty], y\in[0,1] with the following mixed boundary conditions...
I know by definition that if T is a 2nd order tensor and v is a vector,
curl(Tv)=curl(T)v
but what if instead of constant vector v, I have w=grad(u), not constant but obviously an irrotational vector field. Is this still true:
curl(Tw)=curl(T)w ?
My guess is yes since curl(w)=0 but have no...
I have a rough plastic surface that I need to make very conductive. I was thinking of coating it with metal but I do not know how. Would it be possible to dissolve some copper/aluminum/nickel (or others) in acid and then pour the acid on the surface and let it dry? Would that give me a metal...
I want to know what methods there are for calculating forces by a current-carrying coil on a permanent magnet (the application I have in mind is electrical motors). I.e. given a geometry (like a CAD model of the magnet), the magnet type (e.g neodymium), and wire coil geometry, how are the forces...
I am not 100% sure I understand your question but the dependence on the time derivative is there because kinetic energy is a function of it, while potential energy is a function of the position.
If you want a good derivation of Hamilton's principle you can take a look at Goldstein's Classical...
When you have constraints there are many methods of taking care of them. I think that in this case, the simplest is to first write the Lagrangian in terms of x and y, then substitute your constraint equation y(x).
The resulting ODE is for x(t) of your particle. If you want a position function...
Hot mirror is a great suggestion. I just want to make an area invisible to an IR camera but visible to a normal camera.
By the way I was googling around and someone says to spray Copper II sulfate on a piece of glass and that will do the trick. I don't mind the blueish tint and I might give it...
This is what I'm looking for, can you be more specific? How would this be applied to "cooling" ? Cooling of what?
And what chemical reactions would require this, do you have any examples?
Thanks
Hi all,
I want to get some sort of polymer that is opaque to infrared (absorbs wavelengths above 700 nm very well) but transparent to visible light (does not absorb much light below 700 nm).
Does this even exist without being a meta material?
Another grad student and I have figured out a way to create micron-sized channels INSIDE a piece of thermoplastic polymer using a laser. Basically it creates a porous channel inside the material (I attached a microscope image). This is a long channel but the inside of it is not empty - it has a...
I want to give a talk related to calculus of variations. Does anyone know any fun/interesting papers that are somewhat simple to understand?
Could be anything related to calculus of variations, including Lagrangian/Hamiltonian mechanics.
I'm having really bad luck in my search, been trying all...
I don't want to add some crimp because it will heavily increase the time constant. I want to keep response pretty fast (don't we all).
How about I twist them and dip them in a little epoxy? I only need to go to 175C at the most. They will be at room temp 99.9% of their life. Good idea?