Question

Differential equation

Answer 1

I have given this differential equation\[\dot r^2+\dot z^2-2mgz=0\]
and I have to show that z is changing as \[z(t)=\frac{g t^2}{2}\]

I get this if I neglect \[\dot r^2\]. I don't know if I can do that.

Answer 2

is it a PDE?

Answer 3

No, I'm trying to solve some problem in classical mechanics and I got this equation which I have to solve and to get required result. I don't think it's PDE, we haven't do them yet.

Answer 4

if z and r have no dependency on each other I think what u did is right

Answer 5

I'm doing with cylindrical coordinates and position vector is\[\vec r=r \vec e_r+z \vec e_z\]

Answer 6

any success?

Answer 7

no, this is all I've done :/

Answer 8

u must treat r(t) as a constant or find a function that represents z in terms of r(t) according to cylindrical coordinates

Answer 9

can you share the original question from which you got this equation...It might help us solve, not sure how to proceed now

Answer 10

I've got the answer :)
But yes, I can share question and answer with you :)

Answer 11

The answer is

Answer 12

so \[\dot r^2=0\] since r=const. And I don't have it in equation :)

Answer 13

Ohh k ...it makes sense that's the reason I was looking for the original question. Anyway you solved it on your own Good work :)
Not sure if I even remember how to apply angular momentum.

Answer 14

If you are interested in classical mechanics, I can send you few books :)

Answer 15

so you've got the answer!

Answer 16

@avrillavigne yes :) that was so trivial :D

Answer 17

congrats

Answer 18

Thank you but I will pass....Not using much of classical mechanics now days, don't want to have my Irodov days back

Answer 19

in 3 years of studies, classical mechanics was the most interesting subject for me :)

Answer 20

I know It was something I loved in physics....but not sure it will be useful for me to revise now :P