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    Invariance of scalar products on Lie algebras

    Hi folks, If I have a Lie algebra \mathfrak{g} with an invariant (under the adjoint action ad of the Lie algebra) scalar product, what are the conditions that this scalar product is also invariant under the adjoint action Ad of the group? For instance, the Killing form is invariant under...
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    Chern Simons form: calculation

    Hey folks, I'm trying to understand a couple of calculations in Chern-Simons theory and I'm stuck. I want to prove the following in four spacetime dimensions: Let G be a Lie Group with generators T_{a}. Further let A=T_{a} A^{a}_{\mu} dx^{\mu} be a connection and F=dA+A \wedge A its...
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    Fluid model question

    I have a specific question about fluid analysis that is bugging me. I am no expert in this field but very interested in it. Lets's say we want to model a flow where air expands out of an air reservoir across a valve into a cylinder and applies a pressure force on an airtight piston, which...
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    Location-dependent acceleration

    I'm having a really hard time figuring this one out. At first glance it seems very trivial, but I think it is not. This is not a homework assignment but rather a calculation I need to do for personal reasons. The problem is as follows: An object is accelerated along a distance of s. We have...
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    Simulating ballistics

    Hello everyone. I'm new to this forum and very impressed so far. I'm making a program which simulates the flight of an object. In order to do that, I have to compute the coefficient of drag. This is the first problem. From what I know, it should be possible to determine this number (at least...