Laotse

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$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

Laotse

Oct 10, 2019 09:23

I think it's maybe best to ask this multi-part question in the Math.SE itself...

Laotse

Oct 10, 2019 08:36

I know, my description looks messy. I'm just confused, how can we plug d_xi /\ d_pi (which looks to belong to T_(x,p)^T^M) with TM?

Laotse

Oct 10, 2019 08:30

In an easier case, one has covector p from T_x^M and it can be paired with vector v from T_x M. But how do things work in the bundle level?

Laotse

Oct 10, 2019 08:27

A new try. I have seen notations for the canonical two form like d_xi /\ d_pi, so the two form is constucted from the cotangent bundle's coordinates. I don't see, how the two form can map vectors from TM (which are tuples (x,v)), if the two form is NOT constucted from T_x^M, but rather from T^M.

Laotse

Oct 10, 2019 08:19

Ok, I cant type T^M as T star M.

Laotse

Oct 10, 2019 08:16

I'm confused about symplectic forms and Hamiltonian dynamics. If our configuration space is manifold M, then we our phase space is TM. A point q in TM is a tuple (x,p). Now, TM is 2n-dimensional. The question is, where does the symplectic form belong to? Does it map tangent vectors from T(TM) to real numbers or tangent vectors from TM?

Laotse

Oct 10, 2019 08:12

Since it's quiet here, I might ask my second question.

Laotse

Oct 10, 2019 06:55

I would still have another question regarding to differential geometry, but I think I have spammed stupid questions enough...

Laotse

Oct 10, 2019 06:53

Ok, thanks a lot!

Laotse

Oct 10, 2019 06:52

That's what I was thinking about. But if we forget now that it's a misleading vector field and say that we indeed assign R^# vectors on each point of the manifold (which do not belong to T_p), are we then handling with vector bundles?

Laotse

Oct 10, 2019 06:48

Thanks, I'm a beginner at these topics. I still wonder, what is going on in the Wikipedia image, if it cannot be a vector field (some of the vectors are almost perpendicular to the manifold)?

Laotse

Oct 10, 2019 06:44

Where do you refer to?

Laotse

Oct 10, 2019 06:37

Now those vector fields look like to be on TM!

Laotse

Oct 10, 2019 06:35

I'm very new at differential geometry, so is $S^2(\subseteq\Bbb R^3)\to\Bbb R^3$ a vector bundle?

Laotse

Oct 10, 2019 06:33

That's what I wonder. So each vector v should be indeed at T_p? If the vectors are not on T_p, does that image then illustrate then a more general vector bundle than a vector field?

Laotse

Oct 10, 2019 06:25

Thanks for the reply! But I don't understand, how can the vectors on the equator be in T_p, if they point outwards? I don't see now something...

Laotse

Oct 10, 2019 06:16

So if that's not a vector field on S2, then what is it?

Laotse

Oct 10, 2019 06:16

Hello. I wonder, if the figure about vector fields on manifolds on Wikipedia is incorrect: en.wikipedia.org/wiki/Vector_field#Vector_fields_on_manifolds I thought that vector fields "live" on tangent bundles.

Laotse

Jan 29, 2019 08:24

Hello. Is it possible to obtain an approximate solution with method of multiple scales to a nonlinear ODE y''(x) + a - 1/\epsilon*y(x)^2 = 0? I can't get the scales "match".

Laotse

Jun 20, 2018 05:56

Hello. I don't understand the difference between tensor product and Kronecker/outer product. Here (en.wikipedia.org/wiki/Outer_product#Tensor_multiplication) it is said that tensor product of two tensors of order 2 makes a new tensor of order 4. But how is Kronecker product still "tensor product" and it produces still a matrix?

Electrical Engineering

A place to talk with friends from the EE community about vacuu...

Laotse

Apr 17, 2018 18:13

I decided to purchase MCP6041s, again thanks for the Octopart suggestion

Laotse

Apr 17, 2018 17:10

Seems to be available at internet shops and has low input bias

Laotse

Apr 17, 2018 17:10

Found this with Octopart MCP601

Laotse

Apr 17, 2018 16:14

OPA4342 is more rare

Laotse

Apr 17, 2018 16:10

MCP6024 has very low offset voltage and bias current. I think this could be a good op amp for photodiodes! Thanks

Laotse

Apr 17, 2018 16:08

Hmm, both seems to be DIPs, so thah's good

Laotse

Apr 17, 2018 15:50

Can anyone suggest affordable and common rail-to-rail op amps (RRIO) for low bandwidth usage (DIP case)? By low I mean bandwidths at most 100-200 kHz. Operating voltage should include 5V - 0V.

It would be great if bias input current and bias voltage could be as low as possible so the op amp could be used with photodiodes.