/sci/ - Science & Math

>>11513653
>Why would you think you could change my mind by posting a list brain dead religious people? They aren’t smart. If they were smart they would not be religious.
Man you must be breaking down in TEARS by now

>>7903055
>tip

also, your point falls apart when you look at how glorified le nerd culture xd is. Also, at least where I've gone to school, pretty much everyone wishes they were smarter, and the people who are retarded realize and hate it. please keep /r9k/ philosophy bullshit to /b/ so people can screencap it and feel enlightened or something.

>>7289435
>All your ideas are carefully shaped to feed your psycholgical need to believe in a higher power

Page 3 bump

Assuming that the Lagrangian <span class="math">L[/spoiler] is quadratic in the generalized velocities, this is also the general form of the Euler-Lagrange equations, since<div class="math">p^ \mu = \frac { \partial L}{ \partial \dot q^ \mu }</div> is then linear in the velocities, so that<div class="math">\frac { \mathrm d}{ \mathrm dt} \frac { \partial L}{ \partial \dot q^ \kappa }= \frac { \mathrm dp^ \kappa}{ \mathrm dt}= \frac { \partial p^ \kappa}{ \partial \dot q^ \mu } \ddot q^ \mu + \frac { \partial p^ \kappa}{ \partial q^ \mu } \dot q^ \mu</div>and since <span class="math">p^ \kappa[/spoiler] is linear in the velocities, it follows that <span class="math">\displaystyle \frac { \partial p^ \kappa}{ \partial \dot q^ \mu }=A_{ \kappa \mu }(q)[/spoiler] is independent of the velocities and <span class="math">\displaystyle \frac { \partial p^ \kappa}{ \partial q^ \mu } \dot q^ \mu[/spoiler] can be written as a quadratic form of the velocities <span class="math">B^1_{ \kappa \mu \nu }(q) \dot q^ \mu \dot q^ \nu[/spoiler].

Finally, <span class="math">\displaystyle \frac { \partial L}{ \partial q^ \kappa }[/spoiler] must be the sum of a quadratic form of the velocities <span class="math">B^2_{ \kappa \mu \nu }(q) \dot q^ \mu \dot q^ \nu[/spoiler] and a velocity independent term <span class="math">C_ \kappa (q)[/spoiler], and then we let <span class="math">B=B_1-B_2[/spoiler] and recover the form of the differential equation above.

Now since this is the general form of the EL equations, there must be some literature on them, no?
in particular, what is the stability of these and general qualitative behavior?

So a mathematical treatment of the physical equations, basically

How did white people lose their melanin? Can they ever get it back or is it gone forever? pic unrelated

>>5981892

>>5950134