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一、火箭运动的微分方程火箭的运动是属于所謂变貭量运动的范畴的,在飞行过程中,火箭依靠不断噴放高速气流而获得推力,同时,火箭的貭量也就随之減少。为了以后研究方便,我們首先建立起火箭运动的微分方程。 設想火箭是在理想状态下运动,即这时不存在外力的因素。若m为火箭的瞬时貭量,ω为噴气速度(相对于火箭的),火箭在一微小时間dt内向后噴出气体的貭量为dm(为了簡单起見,假定火箭噴气产生的作用力通过火箭的中軸綫,即这时火箭不发生偏轉),那末,由动量守恆定理知:火箭增加的动量mdv应該等于噴气的动量ωdm,但符号相反。于是可得运动方程
First, the differential motion of rockets The motion of rockets belongs to the category of so-called variable enthalpy movements. During the flight process, the rockets rely on continuous ejection of high-speed air currents to obtain thrust. At the same time, the rocket’s enthalpy is also reduced. In order to facilitate future research, we first established differential equations for rocket motion. Imagine that the rocket is moving in an ideal state, that is, there is no external force factor at this time. If m is the instantaneous amount of rockets and ω is the jet speed (relative to the rocket), the amount of gas ejected by the rocket backwards within a small time dt is dm (for the sake of simplicity, it is assumed that rocket jets produce The force passes through the rocket’s central axis, which means that the rocket does not deflect at this time. Then, it is known from the conservation of momentum that the rocket’s increased momentum mdv should be equal to the jet’s momentum, ωdm, but with the opposite sign. Then we have the equation of motion