had a cool lecture from a guy from Reactions Ltd. We started
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had a cool lecture from a guy from Reactions Ltd.
We started off with some deriving of the Rocket Equation, but i missed one crucial part of his logic.
I dont understand how he got rid of dm*dv in this equation.
Any mathmeticians or rocketscientists able to help?
Infinitesimal * infinitesimal = 0. It's part of the so-called "sloppy calculus" used by physicists/engineers. (There is a rigorous way to define calculus using infinitesimals but it's normally done with limits and physicists don't use it anyway.)
dm and dv represent infinitessimal quantities of the mass and the velocity. The value of their product is so small that we can consider it zero.
>>7642033
Why is dm and dv infinitesimal?
Arent they variables - surely they could be anything? or am i being dumb
>>7642039
As a very small period of time, the rocket loses a small amount of mass dm in exchange for an increase in velocity dv.
>>7642060
awesome man, thanks
really 'preciate it
>>7642039
m and v are "variables". dm and dv are differentials, but "variable" isn't a well-defined concept. it just means you haven't assigned a fix value to a quantity
differentials of the form dx can be thought of as infintesimals, and typically there is no need to work with second order in them (i.e. powers >1)
>>7642480
what's the area of a hoop of thickness dr at radius r?
I used this formula in my calc I project to calculate dv produced by the Atlas V lifting new horizons without any timing for staging or accounting for air resistance or dIsp. When one stage was done, it detached and the next fired immediately. Still got about 13km/s relative to earth, so not THAT far off.
>>7642480
Holy shit captain autism, at least we have a stable job in our fields.
https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation