Hello, I am trying to investigate single-stage rockets and I've come across a particular situation I don't know how to handle. The situation I have is that the rocket in question is burning it's fuel not at a constant rate but at a rate [itex]R(\dot{m})[/itex]. So to find the equations of motion shouldn't be much different than for that of a constant rate. Assuming no external forces I should have:
[itex]\frac{dp}{dt}=m_{o}\frac{dv}{dt} + V\frac{dm}{dt} = 0[/itex]
Here, V is given by [itex]V=v-v_{ex}[/itex], where [itex]v_{ex}[/itex] is the velocity of the particulates with respect to the motion of the rocket. But where does [itex]R(\dot{m})[/itex] enter into the picture? Or am I missing something here? Any good references for this type of question? Thanks in advance.
[itex]\frac{dp}{dt}=m_{o}\frac{dv}{dt} + V\frac{dm}{dt} = 0[/itex]
Here, V is given by [itex]V=v-v_{ex}[/itex], where [itex]v_{ex}[/itex] is the velocity of the particulates with respect to the motion of the rocket. But where does [itex]R(\dot{m})[/itex] enter into the picture? Or am I missing something here? Any good references for this type of question? Thanks in advance.