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/sci/ - Science & Math

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9204195 No.9204195 [Reply] [Original]

Question for you nerds

In my physics class I ran across a couple instances of integral manipulation that I am not sure how they did legally mathematically.

I get that dx/dt is velocity and that the dx's "cancel out" leaving v*dv but how are they able to just change the bounds of the definite integral to v? The best thing I could come up with is using u substitution but I couldn't get it to work out.

I asked my prof what formal mathematical rule was used and he just said " I dunno, we just do this in physics a lot, not sure what the rule is"

>> No.9204199
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9204199

>>9204195
And the same thing here

>> No.9204228
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9204228

>>9204195
Think of the path you're integrating through as a path [math]\gamma: [0,1]\rightarrow \mathbb{R}^6[/math] where [math](\mathbb{R}^6,\omega)[/math] is the classical phase space. Time just parameterizes the path, so the total derivative is [math]\frac{dv_i}{dx} = \frac{\partial v_i}{\partial x_k} \dot{x}_k [/math] for coordinate [math]x = x(t)[/math] parameterized by the path [math]\gamma[/math].

>> No.9204247

>>9204195
Velocity can be determined from the x value because its the derivative of the position function. Its just substitution

>>9204228
>muh R6

>> No.9204990

>>9204228
fucking autist briainlet dumb anime fag

>> No.9205149
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9205149

>>9204228
This is literally one of the worst posts I've ever had the displeasure to read on /sci/. There have been a few more painful posts on /int/ so i wont claim on 4chan in general.
I humbly request that you excuse yourself from any environment of interaction with serious and proper mathematicians immediately, and check out the biology department, you fucking shithead physics cuck.