[理工] [工數]-ODE問題

[terrylove12 (風馡)]

題目是成大水利96年考題

An object having mass "m" falls from rest toward the earth from a grate height

under the gravity force with acceleration "g". As it falls, air resistance

acts upon it, and this resistance "Fd" is proportional to the square of the

velocity V, i.e., Fd=α(V^2) . According to the Newton's second law, the

equation of motion for falling object can be written as


 dv
m─ = mg -α(V^2)   with V(0)=0
 dt

Please find the velocity V(t) and the terminal velocity V∞ that is the

velocity at the time approaching infinite.

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 114.36.20.219
推 abcxyz123:分離變數 積分
→ terrylove12:dv=gdt-[α(V^2)/m]dt V平方項 可以請問怎麼丟過去嗎
→ terrylove12:如果丟過去變成 V^(-2)dv=V^(-2)gdt-(α/m)dt
→ terrylove12:還是不能變數分離ˊˋ 還是我有錯誤的地方呢
→ terrylove12:喔喔 找到方法了 但是積分過程很複雜
推 ntust661:很平常的運動方程式@@